The Arsenal forward wants to leave North London and United are favourites for the Dutchman's signature despite rival interest from Manchester City and Juventus.
Rooney has said that he would welcome the chance to play alongside Van Persie.
He told The Mirror: "He's a fantastic player, he's been amazing for Arsenal over many years. If he does come here he would be a great addition to the squad.
"I'd like to think we could play together, but you'd have to ask the manager about that."
Van Persie is currently training with Arsenal in Germany ahead of their friendly with FC Cologne on Sunday, August 12.