The article references one purported offer of a pardon, where CNN claims that
President Donald Trump told Customs and Border Protection Commissioner
Kevin McAleenan he would grant McAleenan a pardon if he were sent to
jail for having border agents block asylum seekers from entering the
US in defiance of US law
The allegation has yet to be substantiated, in particular no potential crime has been identified. Since we're dealing with imaginary scenarios, let us suppose that the CBP Commissioner was offered immunity for ordering agents to shoot asylum seekers on sight (in violation of 18 USC 113, also Texas penal code 22.01). Then the question would be whether this violates 18 USC 373, solicitation to commit a crime of violence. The first part seems clearly applicable:
another person engage in conduct constituting a felony that has as an
element the use, attempted use, or threatened use of physical force
against property or against the person of another in violation of the
laws of the United States
The question turns on whether such an offer constitutes
circumstances strongly corroborative of that intent, (to) solicits,
commands, induces, or otherwise endeavors to persuade such other
person to engage in such conduct
With some creativity, a president could be prosecuted for such an offer, interpreted as an "endeavor to persuade". This assumes that the president forgot to self-pardon before leaving office.
If POTUS were to urge the CBP Commissioner to violate some state law, for example in Texas where (Sec. 7.02)
(a) A person is criminally responsible for an offense committed by
the conduct of another if... (2) acting with intent to promote or
assist the commission of the offense, he solicits, encourages,
directs, aids, or attempts to aid the other person to commit the
offense
then he might have violated Texas law (if an invalid pardon offer constitutes encouragement or an attempt to aid), and in that case he could not self-pardon.