The White House did not immediately respond to a question about the frequency with which Mr. Trump and Mr. Stallone communicate, and a spokeswoman for Mr. Stallone did not return a request for comment. But Mr. Trump seems to have long been fond of Mr. Stallone, an actor most famous for his portrayals of tough guys with machine guns and boxers with inferiority complexes.
In recent years, Mr. Stallone has attended functions at Mar-a-Lago and, like the president, he appears to enjoy signing his autograph in a thick Sharpied scrawl: “Greatest knockout in history!” he wrote to Mr. Trump shortly after the 2016 election.
The president returned the affection and considered bringing Mr. Stallone closer to Washington. Shortly after Mr. Trump was elected, Mr. Stallone said that he had declined being considered for a White House appointment to a post with the National Endowment for the Arts.
Mr. Trump is correct that other presidents did not act on requests to pardon Mr. Johnson, whose dominance as a boxing champion in the early 1900s elicited racial animosity. In 1910, after Mr. Johnson knocked out Jim Jeffries, a white boxer, riots broke out that led to mostly black deaths at the hands of white mobs.
Three years later, a jury convicted Mr. Johnson of transporting his white girlfriend across state lines. He served a year in prison and died in 1946.
The Justice Department does not typically consider posthumous pardons because, according to department guidelines, the time “is better spent on the pardon and commutation requests of living persons.”
But for decades, lawmakers and filmmakers — and, now, a movie star — have tried to persuade presidents to pardon Mr. Johnson. Senator John McCain, Republican of Arizona, and Representative Peter T. King, Republican of New York, have been the most recent legislators to ask.
During nearly every term of Congress since 2004, they have introduced a resolution recommending a pardon. It passed both the House and Senate in 2009 and 2011, but just as Presidents George W. Bush and Bill Clinton before him, President Barack Obama did not grant a pardon.
“Don’t you think this issue says something about the character of America?” Mr. McCain asked The Times in 2015.
According to the Justice Department, Mr. Trump has so far issued three presidential pardons. In August, he pardoned Joe Arpaio, the former Arizona sheriff whose hard-line approach to tamping down on illegal immigration earned him a criminal contempt conviction. In March, he pardoned Kristian Mark Saucier, a Navy submariner jailed after taking unauthorized photographs in a classified area of a submarine.
This month, Mr. Trump pardoned I. Lewis Libby Jr., known as Scooter, who was convicted in 2007 of perjury and obstruction of justice for his involvement in unmasking the identity of Valerie Plame, a C.I.A. officer.
In the time it took to write this article, Mr. Trump, who spent the week mostly ensconced at his Florida properties, had angrily returned to a pet topic: the news media. The president attacked The Washington Post, disputing its reporting that he referred to Jeff Sessions, the attorney general, as “Mr. Magoo” and his deputy, Rod J. Rosenstein, as “Mr. Peepers.”