The duo first met at Vanity Fair's Oscars party last month, reported Us magazine.
"It's just the beginning stage. But they're having a lot of fun and seeing where it goes," a source said.
Evans, 33, previously dated actress Jessica Biel from 2004 to 2006. "The Avengers: Age of Ultron" star most recently split from Minka Kelly for the second time in October 2013. They first parted ways in 2007 before re-connecting in 2012.
Collins, 25, was last linked to Australian actor Thomas Cocquerel in February 2014.
Before that, she dated her "Mortal Instruments: City of Bones" co-star Jamie Campbell Bower, Taylor Lautner, and had a brief romance with Zac Efron.
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