It was not immediately clear whether the president meant he would hold a formal news conference or whether he would simply answer reporters' questions, as he often does, in the Oval Office or as he leaves the White House Thursday afternoon as scheduled to spend the Easter holiday weekend in Florida at his Mar-a-Lago compound.
"You’ll see a lot of very strong things come out tomorrow," Trump said in the interview. "Attorney General Barr is going to be giving a press conference and maybe I’ll do one after that, we’ll see."
Special counsel spokesman Peter Carr told ABC News that Mueller will not appear at the press conference at the Department of Justice and is not expected to issue any statements related to the release of his report.
The Justice Department declined to comment on a New York Times story that reported, "Justice Department officials have had numerous conversations with White House lawyers about the conclusions made by Mr. Mueller."
DOJ spokeswoman Kerri Kupece also said Barr's news conference was pitched and planned by people inside the department. Asked whether the president or the White House made any request that Barr hold a news conference, Kupec replied flatly: "No."
"It was our decision, and it was our idea," Kupec said.
In the radio interview, the president also spoke about the need to ensure that no future president goes through what he has, saying: "I hope I’m going to be able to put this down as one of my great achievements, maybe."
He also offered praise for his new attorney general broadly, saying of Barr that "he’s been a fantastic attorney general, he’s grabbed it by the horn."
Trump also talked about his suspicions that there was spying on his presidential campaign and didn’t rule out that President Barack Obama had knowledge of alleged surveillance.
"I’d rather save that for another interview with you and I," Trump said at first when asked by the host whether he thought the former president had knowledge. "There are those that say ‘how is it possible that he didn’t know?’ I put myself in that category."
"It would certainly be hard to believe that he didn’t know what was going on but we’ll leave that for another day," Trump said.
A Justice official told ABC News that redacted copies of Mueller's report would go to Congress between 11 a.m. and noon.
In an interview with the AP, the president's daughter, Ivanka Trump, said she has "no cause to be concerned" about the pending release of the Mueller report.
A White House adviser, she said that she knew all along there was no collusion and also asserted that she is confident there was no obstruction.
"My opinion of the investigation hasn't changed. I never expressed concern. I never talked about the investigation except when asked. I was fortunate to have knowledge of the fact that I knew that there was no collusion. I knew that there was no obstruction. And this was affirmed in the Mueller report and Attorney General Barr's subsequent summary. So I have no cause to be concerned," she told the AP.
ABC News' Jack Date contributed to this report.