No.
Just no. Not this time. Not running against this president*. Not at this time of national peril. And, for that matter, not this guy. From the AP:
Former Ohio Gov. John Kasich, a Republican and frequent Trump critic, has been approached and is expected to speak at the Democratic National Convention on Biden’s behalf next month, according to a person with direct knowledge of the plans who insisted on anonymity to discuss strategy. Kasich is among a handful of high-profile Republicans likely to become more active in supporting Biden in the fall.