Rosenstein's tenure at the Justice Department has been in question since news reports last month that he'd discussed possibly secretly recording Trump and invoking constitutional provisions to get him removed from office.
Trump had previously said he would prefer not to fire the Justice Department's No. 2 official and that Rosenstein has told him he did not say the remarks attributed to him.
Trump is flying to Orlando for an afternoon address to the International Association of Chiefs of Police Annual convention. "We'll be talking on the plane", Trump said.
Should Rosenstein quit or be fired, his departure would be nearly certain to raise controversy, as he is the top Justice Department official overseeing special counsel Robert Mueller's probe into whether the Trump campaign colluded with Russian Federation to sway the 2016 election.
Mr. Trump has meant to meet with Rosenstein for days, after the New York Times reported that Rosenstein had suggested wiretapping the president and invoking the 25th Amendment - claims Rosenstein denied.
"I didn't know Rod before, but I've gotten to know him", Trump said at the White House.
"I look forward to being with him". And he was very nice.
The reports, which Rosenstein denied, fueled speculation that Rosenstein might be fired or resign.
The president, meanwhile, used part of his speech to rail against Supreme Court Justice Brett Kavanaugh's rocky confirmation process, slamming what he called "false charges" and "false accusations" leveled against him. Advisers had also cautioned Trump against doing anything dramatic in the weeks before the midterm elections next month.
He did not disclose details of their conversation, but referred back to the president's comments as he left the White House saying he did not intend to fire Rosenstein.
Special counsel Robert Mueller's work been overseen by Rosenstein since Attorney General Jeff Sessions recused himself from the investigation. "And we'll see", the president said at a news conference when asked if he would fire the deputy attorney general.
"The press wants to know, 'What did you talk about?'" Trump said at the start of his speech after he thanked Rosenstein for being there and noted the intense media interest.