A source told The Sun newspaper: "As Harry and Cara have hit it off, they thought it would be nice to ask him if he'd sing to her. Whether it's a special rendition of Happy Birthday or something else is undecided. It all depends if Harry has the guts.
"Cara's a decent singer herself so she'd appreciate a tuneful serenade."
The pair were last seen together at Olympic VIP club Omega House in London's West End.
Harry took Cara home after the occasion in his Range Rover car.
Singer Ed Sheeran recently described Harry as "packing heat".
The 'Lego House' hitmaker was given a lift by Harry's band One Direction - made up of Harry, Zayn Malik, Liam Payne, Niall Horan and Louis Tomlinson - back to London after a gig, when he came upon the 18-year-old hunk with no clothes on and was impressed by the size of his manhood.
Ed said: "I turned around and Harry was stripped off and completely naked, just sitting there laughing.
Literally, I was looking out of the window, watching cars go past. I turn around, all the boys are kind of shocked, and there's just him laughing, completely naked."