The 27-year-old actress was first romantically linked to Chris, 34, when they started working together on 2014 movie Captain America: The Winter Soldier.
But the pair dismissed allegations of a relationship as they appeared on The Ellen DeGeneres Show on Monday (02May16).
"Apparently we're dating," Chris said when asked about the romance rumours by the show host.
"But you seem compatible so…" Ellen fished.
Elizabeth then joked: "Well we’ve been dating for like secretly for the last three years... We're actually engaged."
When rumours first emerged that the pair were more than just co-stars, Chris ended up sending Elizabeth a message joking about the claims.
"I remember that," Chris laughed. "I remember sending you a text saying 'Hey guess what apparently we’re dating.' "
"Yeah and I was like 'Oh my god that’s really exciting for us'," Elizabeth giggled. "Yeah. We were about to move in with each other, but we’re still trying to figure out if we’re dating or not, because we don’t talk instead."
Chris concluded: "Yeah. You know that’s what happens."
Despite Chris and Elizabeth's determination to dismiss the romance rumours, Ellen seemed keen to draw their attention to the chemistry they have - both on and off screen.
"I don’t know. I’m just saying," Ellen smiled. "Think about it, don’t just poo, poo it. I mean you’re both single. And if they’re saying it, maybe somebody sees something you don’t."
Elizabeth reprises her role as Scarlet Witch/ Wanda Maximoff in the new movie Captain America: Civil War, with Chris once again playing the shield-wielding superhero.
The Marvel world sees the heroes star alongside each other in collaborative films such as Captain America or Avengers, as well as standalone films.
Rumours have been swirling for some time about a Scarlet Witch spin off film, but Elizabeth isn't sure she'd be up for it.
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