“He’s in self-pity mode,” the source told the broadcaster.
On the other hand, the view among a number of those who are close to the US president is that “his actions led to here, no one else,” the source explained.
“He instigated a mob to charge on the Capitol building to stop decertification, he’s not going to find a lot of sympathetic Republicans.”
The White House did not immediately respond to The Independent’s request for comment on the claims.
The siege on the Capitol has been particularly divisive within the Republican party and has led a number of Mr Trump’s ardent supporters to turn their backs on him.
During the siege, pro-Trump supporters breached the Capitol, vandalising property, looting offices, and overwhelming the building’s security, forcing lawmakers to evacuate.
Supporters marched to the Capitol following encouragement from the president, who told them to “show strength” and fight for him at a “Save America” rally beforehand.
Five people died as a result of the violence including one Capitol police officer who was beaten as he tried to ward off the crowds.
On Wednesday, 10 House Republicans voted to impeach Mr Trump, turning against the president and their party to join with Democrats seeking his removal from office for a second time in a historic blow.
Going forward, at least four Republican senators have indicated they were either undecided or considering supporting impeachment, including majority leader Mitch McConnell.
During the last impeachment effort, Mr Trump’s allies staunchly defended the president, sending out talking points throughout the proceedings.
Now, the president is becoming increasingly isolated, with a swathe of White House officials having walked out on the administration following the riots, including the transportation secretary, Elaine Chao.
The president has also been banned from major social media networks, including Twitter, limiting his platform to hit out at proceedings or undermine them.
On the White House’s official Twitter account on Thursday, Mr Trump released a video saying he “unequivocally condemns” the Capitol riot violence in an attempt to distance himself from the insurrection.
The president has just seven days remaining at the White House before the president-elect, Joe Biden, is inaugurated on 20 January.
While the president is unlikely to be impeached during this time, the trial could impact any plans the president may have had to run for office again in 2024.
According to a report by The New York Times, some of the president’s advisers have suggested he resign a few days before his term ends in order to avoid the risk of conviction and being barred from running in 2024.
However, according to the same report, he has been dismissive of any suggestion that he leave the presidency early, suggesting it would further impact his influence within the GOP.
Democrats will need at least 17 Republicans to join them to remove Mr Trump from public office for good and uncertainty lingers on where many within the Senate GOP will stand on a conviction.