Rooney has been the subject of transfer speculation all summer, amid interest from Chelsea.
"Everyone wants Wayne to stay," Van Persie told The Sun. "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 and 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."
Rooney will not be part of the United squad that will take on Wigan Athletic in the Community Shield today.