You should assume that the logo in question is a registered trademark. This, for example, indicates that the baseball plus diamond with "ESPN" is "live". Some former trademarks like this are "dead" (abandoned). That means those are federally registered, and they are entitled to use the ® symbol. But, even without registration, there is "common law trademarking" notated ™. There is a risk that you would be sued for infringement. The main question is whether there is confusingly similarity between your logo and theirs. One way to negate that risk is to request permission to use the trademark from the owner (probably Disney). There is also a concept of "fair use", which you could use in court to defend yourself. There is a concept of nominative use, discussed at scholarly brevity in this article, and one of the cases that the concept rests on is Brother Records v. Jardine. A crucial feature is that under such possibly-permitted usage, you would use (future) plaintiff's logo to describe their product. (This concept exists in the US 9th Circuit). There is also jurisdictionally-broader generic fair use, described here, which is useful in giving examples of cases where "fair use" was found versus was not found. One of the latter cases is Corp. of Gonzaga Univiversity v. Pendleton Enterprises, LLC where (according to inta.org) the infringement "did not constitute nominative fair use because there were numerous ways in which the radio station could have entertained its Gonzaga fans without infringing plaintiff’s trademark".
You should bear in mind that sports logos are marketable objects, and hundreds of millions of dollars can be made by licensing the right to use the logo.
At a minimum, you should seek the expert opinion of an IP attorney, who could say e.g. "It is virtually guaranteed that you will get sued" vs. "I can't imagine that they would sue you", or something in between.