The Jonas Brothers sensation sparked gossip that he had sunk his teeth into the star, who plays vampire Alice Cullen in the hit franchise. They were spotted on a dinner date in London last month.
And the pair has kept in touch: They were spotted chatting and laughing near Greene's apartment on last week before heading for a nearby mall and picking up coffee.
Greene is the latest teen pinup the singer has been linked to. He has previously dated Taylor Swift and Demi Lovato.