The president is expected to meet with Senate Majority Leader Mike Shirkey and House Speaker Lee Chatfield -- both Republicans -- at the White House after requesting the visit, the sources said.
The move comes amid the Trump campaign's ongoing fight over the outcome of the election in the battleground, with relentless unsubstantiated claims of fraud and a string of, so far, unsuccessful legal challenges to the results.
The White House declined to comment on whether the meeting would take place.
In a press conference Thursday, President-elect Joe Biden said Trump's actions are going to be "another incident where he will go down in history as being one of the most irresponsible presidents in American history."
"It's just out of the -- not even within the norm at all," Biden added. "There's questions whether it's even legal. But it's going to be interesting to see who shows up in this call to meet with the leadership."
Trump's effort to pursue a pressure campaign ahead of the state's board of canvassers meeting on Monday, regardless if successful, is actively sowing doubt in the integrity of the election.
His brazen gambit in a state where he is trailing by the widest margin among the battlegrounds -- more than 150,000 votes -- follows a chaotic 48 hours in Michigan. The certification process in the state's largest county was thrown into turmoil by repeated reversals from two Republican members of the county board of canvassers.
It also comes after members of his own legal team have openly suggested that their last recourse might be a GOP-controlled legislature intervening by overturning the will of the people and choosing their own slate of pro-Trump electors to vote for the president at the Electoral College's December meeting.
The prospect of the Michigan Legislature intervening in a process that by state law they are not involved in is not one that has been publicly embraced in Lansing.
Shirkey told Bridge Michigan, a local news outlet, "that's not going to happen," and a spokesperson for Chatfield has told ABC News that the speaker has been clear about his position that the person who receives the most votes in Michigan will receive Michigan's electoral votes.
A spokesperson for the state Senate majority leader also reiterated that state law does not allow for the legislature to step in and directly select the electors or award the electors to anyone other than the popular-vote winner.
If the state legislature were to appoint pro-Trump electors, under pressure from the president, Samuel Bagenstos, a professor of law at the University of Michigan, who specializes in constitutional law, said it would be an "outrageous subversion of democracy."
Trump's increased public involvement, and the chaos in Wayne County, brought Monday's vote to certify the statewide results to the fore.
The bipartisan state board of canvassers, which is made up of two Republicans and two Democrats, are set to meet to finalize the election. Only three votes out of four are needed to officially verify the results.
One Republican member of the state board, Norm Shinkle, a longtime Republican activist from Ingham County, told Bridge Michigan that he is making "no predictions" about the impending vote.
Shinkle hasn't ruled out affirming the results, but his wife, Mary Shinkle, who served as a Republican poll challenger in Detroit, filed an affidavit as part of the Trump campaign's lawsuit in the state, according to the Detroit Free Press. He also told the outlet he had concerns over what his wife saw while watching the tallying of the votes.
The other GOP member of the board, Aaron Van Langevelde -- appointed by former Gov. Rick Snyder in 2018 -- has not publicly signaled how he will vote.
But after the spectacle in Wayne County, in which the local elections board was briefly deadlocked on Tuesday night before reversing course and certifying the results just hours later, there are concerns within the state about the possibility of the state board coming to an impasse, which would punt the process to the courts, Bagenstos said.
"The state courts have in the past ordered members of the state board of canvassers to do their legal duty. And I fully expect that if they're called on to do that this time, they will order the canvassers to do their legal duty and certify the election because there is no legal basis for refusing to certify the election right now," he said.
Further complicating Monday's vote is the decision by the two Republican canvassers in Wayne County to seek to rescind their vote to certify a day after the deadline.
All 83 counties in Michigan have certified their results, according to the secretary of state, whose office dismissed the latest turn in a dramatic series of events in Wayne County.
"There is no legal mechanism for them to rescind their vote," a spokesperson for Secretary of State Jocelyn Benson said. "Their job is done and the next step in the process is for the Board of State Canvassers to meet and certify."
Benson reiterated on Thursday night in an interview with ABC News Live that there has been "no evidence of widespread fraud in the election."
Legal experts, too, believe that the final vote on Tuesday is in fact final.
"The Tuesday night vote to certify is the final vote. That's the legally applicable vote," said Bagenstos. "The affidavits that these couple of canvassers filed don't have any legal effect on the vote ... they would have to have a new meeting."
Both GOP members of the board, Monica Palmer and William Hartmann, spoke with the president the evening before they disavowed their vote certify the results, sources told ABC News.
It's not immediately clear if the latest move to reverse their votes was discussed. ABC News has reached out to both Palmer and Hartmann.
ABC News' Ben Gittleson, Molly Nagle and Adia Robinson contributed to this report.
This report was featured in the Friday, Nov. 20, 2020, episode of “Start Here,” ABC News’ daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.