The England international's Old Trafford future has been up in the air ever since former manager Sir Alex Ferguson claimed in May that he had asked to leave.
Rooney's situation remains unclear three months on, with new manager David Moyes yet to call on the 27-year-old, who will also miss Sunday's Community Shield with Wigan.
Chelsea have made two unsuccessful bids for Rooney, who was understood to be "angry and confused" at comments made by Moyes that Van Persie is his number-one attacking option.
But the Dutchman hopes that Rooney can work a way through whatever issues he may have. He told The Sun: "Everyone wants Wayne to stay and deep down I think he feels the same. One of the reasons I joined Manchester United was to play with Wayne.
"I hope he stays. Not only is he a great goalscorer, he does so much work across the pitch. He hates to lose - that's why you see him one minute pressing for goal, the next minute defending ferociously.
"He is an asset to any team. He will come good again. He is a strong lad."
Moyes on Saturday night moved to smooth talk of a rift with the player he also coached at Everton.
The shoulder injury which United have cited him as having has not stopped him being picked for England's meeting with Scotland on Wednesday, and a pointed Facebook statement from Rooney, which thanked national boss Roy Hodgson for the faith he had shown in him while omitting any mention of Moyes or United, was taken as further proof that all is not well.
However, while the position is far from ideal given Rooney's desire to leave and his time spent training with the reserves this week, Moyes has indicated the rift is not quite as bad as some have claimed.