Mr Trump was impeached for an unprecedented second time by the House for inciting the deadly Capitol riot, and now Nancy Pelosi will transmit the articles to the Senate on Monday for a trial.
The lobbying effort is reportedly concentrated on Senator Mitch McConnell, the Senate minority leader, who has privately signalled he may support convicting Mr Trump.
Mr McConnell’s decision is likely to have significant influence over the caucus he has led for 14 years.
“Mitch said to me he wants Trump gone,” one Republican member of Congress told CNN.
“It is in his political interests to have him gone. It is in the GOP interest to have him gone. The question is do we get there?”
In order to convict Mr Trump 17 Republicans in the Senate would have to join the 50 Democrats expected to vote against him.
If convicted the Senate would then vote on whether to ban Mr Trump from holding office again.
And some Republican insiders say that convicting Mr Trump is essential for the future of the GOP.
"Trump created a cult of personality that is hard to dismantle. Conviction could do that,” a former senior Republican official told the news network.
A nine-point memo has reportedly been circulated among senior Republicans that says, “it is difficult to find a more anti-conservative outburst by a US president than Donald Trump the last two months.”
It also states that Mr Trump encouraged the crowd at his 6 January “Stop the Steal” rally, which was “widely understood to include people who were planning to fight physically, and who were prepared to die in response to his false claims of a ‘stolen election.’”
The memo also points out that Mr Trump was tweeting about his vice president, “as the Secret Service was being forced to rush Mike Pence out of the Senate chamber and into a protective bunker.”
Senator Lindsey Graham told Fox News earlier this week that anyone wanting to dump Mr Trump from the Republican Party would “get erased.”
"This idea of moving forward without Donald Trump in the Republican Party is a disaster for the Republican Party,” said Mr Graham.