The president also said he doesn't "know the situation" regarding Prince Andrew, who federal prosecutors accuse of not responding to their attempts to discuss the case.
Asked during his first White House coronavirus press briefing since April about the Ms Maxwell's alleged role in the sex trafficking conspiracy, the president said he knew her from their time in Palm Beach, Florida, and that they've met "numerous times."
A reporter asked the president whether he believed Maxwell was going to "turn in powerful men" as she faces trial.
"I don't know, I haven't really been following it too much," he said. "I just wish her well, frankly. I've met her numerous times over the years, especially since I lived in Palm Beach and I guess they lived in Palm Beach. But I wish her well, whatever it is. I don't know the situation with Prince Andrew, I just don't know. Not aware of it."
Maxwell helped billionaire Epstein "recruit, groom and ultimately abuse" victims they knew were under the age of 18, according to charges filed in a six-count indictment on 2 July, which followed years of accusations from their alleged victims.
She has pleaded not guilty to the charges against her and will remain in prison ahead of a trial, which is not likely to begin until next year.
A tentative trial date has been set for 12 July 2021.
During a 14 July hearing, US District Judge Alison Nathan denied Maxwell's bond, citing "extraordinary financial resources which could provide her the means to flee the country" despite Covid-19-related restrictions in place.
"No combination of conditions could reasonably ensure her presence at court," Judge Nathan added. "The risks are simply too great."
The court also heard from two alleged victims speaking in support of prosecutors' argument to deny Maxwell's bail.
The alleged victims described Maxwell as a predator who groomed and abused "countless" young women me and "has never shown any remorse for her heinous crimes".
A statement from another victim, who gave the alias Jane Doe, called her a "predator and a monster".
Maxwell was arrested nearly a year after Epstein allegedly killed himself in jail while awaiting trial on federal sex trafficking charges.
The Duke of York has previously been targetted by former US attorney Geoffrey Berman – who was recently and controversially removed from his post by US attorney general William Barr – over allegations that Andrew has refused to cooperate in the case.
Acting US attorney Audrey Strauss has sought his cooperation in Maxwell's case.
"We would like to have the benefit of his statement," he said.
While the president's allies and right-wing conspiracy theorists have pointed to Epstein's ties to former president Bill Clinton and other Democrats, they also have downplayed Trump's long-standing relationships with Epstein and Maxwell.
Prince Andrew has said he is willing to cooperate with US authorities, but the US attorney's office has said he has "shut the door" in cooperating with law enforcement. Prince Andrew's legal team previously told The Independent that "the Duke's team remains bewildered given that we have twice communicated with the [Department of Justice] in the last month, and to date, we have had no response".