The senate majority leader has told associates that he is happy Democrats have moved to impeach Mr Trump as it will make it easier to re-build the Republican party, according to the New York Times.
The president will face charges that he incited violence against the country.
The vote would come exactly a week after the Trump riot that saw his supporters storm the US Capitol to try and prevent Joe Biden’s election victory being certified by lawmakers.
Mr McConnell, a senator from Kentucky, reportedly blames Mr Trump for Republicans losing control of the senate after the Georgia runoff election put Democrats in control of the tied high chamber.
Five people, including a US Capitol police officer, were killed in the mayhem that followed Mr Trump’s rally where he urged them to march on Capitol Hill.
After a lengthy delay caused by the chaotic scenes the House and Senate reconvened and confirmed Mr Biden’s win over Mr Trump.
House minority leader, Kevin McCarthy, has also asked his GOP colleagues if he should call on Mr Trump to resign, Republican officials told the New York Times.
Mr McCarthy is reportedly against impeachment but he and Republican leaders will not lobby for a “no” vote on the issue.
Earlier Mr Trump gave his first live speech since the violence and called his supporters who stormed the building a “mob.”
But Mr Trump also warned Democrats not to remove him from office in his final days, through either the 25th amendment or impeachment.
“It’s causing tremendous anger and division and pain far greater than most people will ever understand, which is very dangerous for the USA, especially at this very tender time,” Mr Trump said on Tuesday at a segment of the US-Mexico border wall in Alamo, Texas.
Mitch McConnell has not yet returned a request for comment.
Subscribe to Independent Premium to bookmark this article
Want to bookmark your favourite articles and stories to read or reference later? Start your Independent Premium subscription today.
Already subscribed? Log in