Sources told TMZ the 30-year-old actress has known the 45-year-old Tesla founder for years and has been spending "a lot of time" with him over the past few months.
Insiders said Heard had dinner at Musk's house this month in Los Angeles and recently visited him at his office. Musk has reportedly also stopped by Heard's home and saw the actress in Miami last weekend.
Page Six reported Musk, also the CEO of SpaceX, was in Florida for a rocket launch from Cape Canaveral. Sources said Musk and Heard stayed in separate rooms at the Delano Hotel but were seen entering and exiting the same room at several points.
"They were seen arriving to, and leaving, the same room many times, but always separately," an insider said. "He was seen going in at night and doing a 'walk of shame' in the morning."
Musk's rep told the website they believed the sources were "mistaken." The spokesperson dismissed the CEO's reported "walk of shame" by saying, "Don't think that last bit is true, unfortunately."
Heard is in the midst of divorcing Depp. She filed to end her marriage in May and subsequently accused the actor of abuse while seeking a temporary restraining order. The order was reissued in June, while a hearing for the case has been pushed back to August.