Trump has been busy making calls to allies in the Senate and other supporters to gauge if they too felt it was time for a leadership change, people familiar with the conversations told the Wall Street Journal.
But lawmakers and their aides say there's apparently little interest in finding a Kentucky Republican to run against McConnell.
However, they added that even having the conversations will likely further deepen the divide between the two Republican leaders - one a reigning establishment figure with more than three decades in the Senate, the other a former president who still has outsized influence on the party.
DailyMail.com has reached out to McConnell's campaign for comment.
Trump wouldn't tell the Wall Street Journal whether he was personally scoping the field for a potential challenger.
But he said Senate Republicans 'ought to' push him out themselves.
'I think he's very bad for the Republican Party,' Trump said.
Former President Trump is reportedly looking for someone to mount a primary challenge against Senate Minority Leader Mitch McConnell, though he denied personally scouting for candidates himself
And with President Joe Biden's approval rating continuing to slip, the GOP is looking for the path forward to seize on Democrats' weaknesses.
In Congress, it appears even Trump allies are toeing party line for now.
Alabama Senator Tommy Tuberville, who was endorsed and lauded by Trump, shied away from defending the former president.
'I'm not going to get in that fight,' Tuberville told the Wall Street Journal, adding that McConnell 'is doing a good job.'
Senator John Kennedy of Louisiana, also a Trump supporter, told the outlet Trump's chances of ousting McConnell are close to that of a donkey learning to fly.
'I just don't realistically see that happening,' Kennedy said.
It's the latest shot taken in the Trump-McConnell rift, which has only grown since the former president lost in