The story adds more clarity to comments the president made Wednesday about Rosenstein and Mueller, whom he has repeatedly criticized. Asked whether he had "concluded it is not worth the political fallout" to oust either official, Trump did not directly answer.

Last week, Deputy Attorney General Rod Rosenstein told the president he is not a "target" of special counsel Robert Mueller 's investigation into Russian efforts to influence the 2016 election, Bloomberg reported Thursday. After the White House meeting last week, Trump told confidants he does not want to fire Rosenstein or Mueller right now, according to the report.

President Donald Trump has appeared to back off two key figures in the Russia investigation, for now.

"They've been saying I'm going to get rid of them for the last three months, four months, five months, and they're still here. We want to get the investigations over with, done with, behind us," the president said at a joint press conference in Florida with visiting Japanese Prime Minister Shinzo Abe.

Still, Trump's current stance on firing Rosenstein and Mueller does not mean he will not try to remove them in the future.

Mueller is investigating Russian meddling in the election and whether the Trump campaign coordinated with Moscow. Rosenstein, who has led the investigation since Attorney General Jeff Sessions recused himself from it, put Mueller on the job.

Removing one or both officials could take away the cloud of the investigation, which Trump has repeatedly called a "hoax" and "witch hunt." But it could also bring backlash from members of Congress or voters.

Ty Cobb, the White House lawyer working on the Russia probe, told CNBC that the president is not considering firing Rosenstein and Mueller.