The heartthrob was spotted leaving Greene's apartment in the morning and later went shopping with the actress who plays vampire Alice Cullen in the cult film franchise, reported Daily Mail online.
The singer who is part of the pop trio 'Jonas Brothers' has previously dated a string of beauties, including Taylor Swift, Demi Lovato and Camilla Belle.
The couple were spotted leaving Greene's LA apartment yesterday morning, doing a spot of shopping at a nearby mall and grabbing a cup of coffee together.
Looking relaxed together, the pair smiled and talked, but kept a safe distance as they walked from the car to the coffee shop.
Greene, 23, and Jonas, 20, were first linked last month after they dined together at The Ivy in London and also attended a 'Kings Of Leon' gig together.
Despite their string of dates in recent weeks, friends of the stars claim they are just friends.
Jonas has been single since splitting from 'Camp Rock' co-star Lovato in May after a brief romance.
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