The pair reportedly got close while playing husband and wife in their upcoming biopic, I Saw The Light, in which Hiddleston plays singer-songwriter Hank Williams. They also, of course, have the Marvel connection -- the British actor plays Loki in the Avengers and Thor films, while Elizabeth made her debut as the Scarlet Witch in Avengers: Age of Ultron.
Olsen called off her engagement to actor Boyd Holbrook in January.
"She wants to make a new life for herself," the source says. "She's having fun."