The singer-actor, who has described ex-girlfriend Jessica Biel as the "most significant" person in his life, took Olsen to the Saturday Night Live after-party following his hosting stint two weeks ago, as well to a polo match and two Broadway shows, a source told Us Weekly.
"They are hooking up," the insider claimed.
Timberlake and Olsen apparently hope to keep their romance "on the down-low" in order to avoid attention from the media, a second source indicated.
A rep for Timberlake confirmed that the two are "friends", but denied that the Friends with Benefits star and Olsen are "romantically involved".
Olsen recently split from Hangover Part II actor Justin Bartha after dating for nearly three years.
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Watch the Friends with Benefits trailer below: