The Dutchman revealed in July that he would not sign a new contract at the Emirates, citing a disagreement "in the way Arsenal should move forward" and speculation over his future has been rife ever since.
Although Van Persie missed the club's Asia tour, he flew out to Germany on Monday for a week-long training camp, suggesting a potential move is far from certain. Indeed, claims that the demands of his agent looked as if they would scupper the move to Manchester surfaced on Thursday.
Despite this, Rooney was happy to speak about a potential move for the Arsenal captain.
"Of course he's a player that I admire," Rooney told the Daily Mail.
"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 whether he could play alongside Van Persie, 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.
|15/2||Wayne Rooney is 15/2 with bet365 to be the top Premier League goalscorer in 2012-13|
"So there's a lot of forwards fighting for a place."
Sir Alex confirmed on Wednesday that United had made an offer for Van Persie but revealed there had been no breakthrough with Arsenal.
United have just one game remaining in their pre-season schedule against German side Hannover on Saturday after drawing 0-0 with Barcelona in a glamour friendly in Gothenburg on Wednesday.
Rooney was substituted at half-time having missed a penalty in the first half and the forward commented: "I'm not sure why that was, you’d have to ask the manager.
"I think he felt some other players needed minutes. But I'm excited, I feel good, I feel fresh and I'm looking forward to the new season.
"It's a big season for us after last season and we all need to be ready for it.
"It was a good work-out. I would have obviously liked a bit longer but it was a chance for some of the players to get some more game time.
"It was a good result - disappointing to lose on penalties but a good run-out."