The magazine reports that the "Captain America" star, 33, and the "Mortal Instruments: City of Bones" actress, 25, have been seeing each another for about a month since meeting at Vanity Fair's annual Oscar party on Feb. 22.
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"It's just the beginning stages," an insider told Us. "But they're having a lot of fun and seeing where it goes."
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Neither is a stranger to Hollywood romance: Evans has dated Jessica Biel and Minka Kelly (and in 2014 was linked to Sandra Bullock), while Collins -- who's the daughter of Genesis rocker Phil Collins -- was once hot and heavy with Jamie Campbell Bower, Taylor Lautner and Zac Efron.