Statements of jurors about their deliberations are not allowed to be considered for any purpose, subject to very narrow limitations which do not apply in the fact pattern you are asking about in this question.
The General Rule And Its Exceptions
Consideration of juror statements, subject to narrow exceptions, is barred by Federal Rule of Evidence 606(b), which has a state or territorial equivalent that is substantially similar in every U.S. jurisdiction that has true jury trials (as opposed, for example, to courts-martial which look like jury trials but are not jury trials from a legal doctrine perspective). Federal Rule of Evidence 606, which is the model for the lion's share of these rules reads as follows:
Rule 606. Juror
(a) At the Trial. A juror may not testify as a witness before the
other jurors at the trial. If a juror is called to testify, the court
must give a party an opportunity to object outside the jury’s
(b) During an Inquiry into the Validity of a Verdict or Indictment.
(1) Prohibited Testimony or Other Evidence. During an inquiry into the
validity of a verdict or indictment, a juror may not testify about any
statement made or incident that occurred during the jury’s
deliberations; the effect of anything on that juror’s or another
juror’s vote; or any juror’s mental processes concerning the verdict
or indictment. The court may not receive a juror’s affidavit or
evidence of a juror’s statement on these matters.
(2) Exceptions. A juror may testify about whether:
(A) extraneous prejudicial information was improperly brought to the
(B) an outside influence was improperly brought to bear on any juror;
(C) a mistake was made in entering the verdict on the verdict form.
This is subject to exceptions only in a few extremely limited circumstances:
To document interference or influence on the jury from outside the jury during the trial or deliberations (e.g. bribery of a juror, a juror's consultation of outside facts, blackmail of a juror, counsel for a party providing information not authorized by the judge to the juror). This is covered by Rule 606(b)(2)(A) and 606(b)(2)(B).
To establish that a mistake was made filling out the verdict form (e.g. testimony immediately following a jury trial that the jurors confused the names of two co-defendants and incorrectly filled out the jury form convicting each one of the crimes where the jury found the other co-defendant guilty). This is covered by Rule 606(b)(2)(C).
Under an exception created just this year for the first time (the source opinion of the U.S. Supreme Court by a 5-3 vote in this case, Peña-Rodriguez v. Colorado (March 6, 2017), is here), to document that one or more jurors essential to the verdict reached the result as a result of a racially/ethnically discriminatory reasons (e.g., one or more of the jurors who voted to convict in a case resulting in a conviction said "let's convict him because he's Hispanic" and then did so). This is not expressly covered by Rule 606(b), but the U.S. Supreme Court held that it is constitutionally necessary to allow it.
The situation you pose does not involve any of these exceptions. Instead, it concerns the internal deliberations of a jury not subject to outside influence, and it does not involve racial or ethnic bias in deliberations. So, this information is legally irrelevant and may not be considered by any court at the trial or appellate level.
Procedural Aspects Of This Question
Of course, in all of these scenarios including the exceptions, the mere fact that a juror says something publicly is meaningless legally. But, there is no means by which a lawyer in a case (or anyone else) can obtain information about juror deliberations through a subpoena or other compulsory court process. The only way anyone could find out about improper jury deliberations is if a juror voluntarily discloses these facts.
Any effort to introduce consideration to this statement would have to be submitted to the trial court (generally, the trial court that handled the original case, but sometimes a habeas corpus action trial court) in either the form of a sworn affidavit of the juror, or live witness testimony of the juror under oath in the trial court in a post-trial hearing of some sort.
This would have to be submitted by a lawyer for the defendant (or less often by the prosecutor in the case, seeking to right a wrong discovered by the prosecutor, for example, in the context of a separate bribery investigation conducted by the prosecutor's office). The juror or a third-party would not have standing to challenge the verdict or to bring juror statements to the court's attention in a legally effective manner.
A statement of a juror about the verdict or how it came to be at a trial can only be considered at the trial court level and only:
(i) in a post-trial motion for a new trial, which can be considered on direct appeal,
(ii) in a collateral attack on the original verdict in a different kind of post-trial motion (state practice differs regarding what these motions are called), or
(iii) in a collateral attack through a separate civil action (called a habeas corpus action) to set aside a jury verdict.
Generally speaking, appellate courts never consider new evidence in any kind of case and can only consider evidence that is part of the official trial court record. The only true exception to this rule is that it may consider a post-trial fact that would terminate the case for procedural reasons (e.g. the existence of a settlement by the parties, or the death of a defendant during the pendency of the appeal or earlier which would render the appeal moot).
Appellate courts can take "judicial notice" of certain matters that constitute general knowledge not specific to the case before them (e.g. the existence and duration of the U.S. Civil War, or the distance between New York City and Chicago, or the name of elected officials at the time the facts of the case took place). But, evidence concerning juror statements is not something about which judicial notice may be taken.
Why do we have such a rule when allowing this testimony could prevent serious miscarriages of justice?
In rough order of importance, the reasons include the following:
To protect the ability of a jury to engage in "jury nullification", which is an issue also informed by the double jeopardy protections of the 5th Amendment to United States Constitution (applied to state and local proceedings by virtue of incorporation through the 14th Amendment to the United States Constitution and parallel state constitutional protections) against revisiting a jury acquittal in a criminal case for any reason.
To minimize the burden jury service places on jurors who would otherwise routinely be interrogated by lawyers unhappy with their verdict after the trial even if they didn't want to speak with those lawyers.
To protect the finality of verdicts on appeal and in post-trial proceedings as this would add another set of grounds to disturb a court decision in addition to those which can be observed in the court record.
Non-Obvious Consequences Of This Rule
One important consequence of this rule is that "harmless error" analysis by an appellate court, which is conducted when there is a legal error made in a jury trial to determine if the error, if it had been corrected, was material enough to change the outcome of the case, is always conducted on a hypothetical and theoretical basis rather than based upon actual factual knowledge of what would have or would not have influenced the jury's decision.
Another important consequence of this rule for appellate practice is that jury verdicts will be upheld in any case where it would be possible for the trial court record to allow a jury to come to the conclusion that it did, whether or not the jury actually considered the arguments and facts it would have had to have considered to correctly reach its verdict. Thus, it is frequently the case that a jury misunderstands the jury instructions or the facts of the case and makes an incorrect decision as a result, but that verdict is upheld on appeal because it would have been possible for a jury which, for example, found witnesses that the actual did not actually believe were telling the truth to have been truthful to rule in the manner that it did.
Another practical effect of this rule is that it is easier to overturn a judge's decision on appeal because the judge must articulate his or her factual and legal basis for each ruling, than it is to overturn a jury verdict, since a jury need not articulate the reasoning behind its verdict except to the extent that it is given and completes special verdict forms when it deliberates.