WASHINGTON—President Trump said Wednesday that his campaign might be willing to accept information from foreign governments that was damaging to his 2020 rivals, adding that he might not divulge such information to the FBI.

“It’s not an interference, they have information—I think I’d take it,” Mr. Trump said in an interview with ABC News. “If I thought there was something wrong, I’d go maybe to the FBI—if I thought there was something wrong.”

But...