(CNN) -- Jared Kushner, President Donald Trump's son-in-law and senior adviser, has approached the President about conceding the election, two sources told CNN.
The move follows Trump's assertion in a statement from his campaign -- moments after CNN and other networks projected that Joe Biden will become the 46th President of the United States -- that Biden is "rushing to falsely pose as the winner" and that the race is "far from over."
"I will not rest until the American People have the honest vote count they deserve and that Democracy demands," Trump said in the statement, which explains that the campaign's legal battle will begin Monday.
Biden-Harris deputy campaign manager Kate Bedingfield said Saturday night that there had been no communication between Biden and Trump, or between any representatives from either campaign, since the race was called earlier in the day.
And Biden campaign senior adviser Symone Sanders, told CNN's Jake Tapper on "State of The Union" Sunday that "a number of Republicans from the Hill have reached out," but said, "I don't believe anyone from the White House has."
Biden won the presidency Saturday after the battleground state of Pennsylvania pushed the Democrat over the 270 electoral votes needed to capture the White House.
Trump, who was at his golf course in Sterling, Virginia, on Saturday when the race was called, has not denied the outcome of the election, privately at least, sources told CNN. But he's continuing to push his attorneys to pursue legal challenges that would delay formal certification of the results.
White House chief of staff Mark Meadows, who recently tested positive for coronavirus, discussed next steps with the legal team Saturday.
CNN's Betsy Klein, Keith Allen and Chandelis Duster contributed to this report.