Chelsea have made two unsuccessful bids for Rooney this summer.
But Van Persie 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."
For the big stories and the banter follow us on Twitter: @tribalfootball