"Of course he's a player that I admire," Rooney said in the Daily Mirror.
"He's a fantastic player. He's been amazing for Arsenal over many years. Last season was probably his best season of all. He scored a lot of goals.
"If he does come here he would be a great addition to the squad."
Asked if he and Van Persie could play together, Rooney added: "I'd like to think so - but you'd have to ask the manager about that.
"There's a lot of forwards here already with myself, [Danny] Welbeck, Chicharito and [Dimitar] Berbatov, who's still here.
"So there's a lot of forwards fighting for a place."