Run for president on what platform? Genuinely, was he planning on running against Trump or against Biden?
Because both parties see him as a traitor. To Democrats, he was the lone senator blocking pivotal congressional action for years. To Republicans, he's been sleeping with the enemy and pushed out what would have otherwise been a guaranteed seat in the senate so he could be a "compromise Democrat".
He was being courted by the No Labels group. He wasn't going to win against Trump or Biden, but might have siphoned off several percent of voters who would otherwise go for Biden, throwing the election to Trump. Which was the whole point of trying to get him to run.
Thank you for the actual answer. I still think that's really stupid though, as you'd have to be a fool to vote for him on his record in congress. I think it's just as likely he'd siphon votes from Trump in that case.