Stubbs has seen Rooney grow from boy to superman after celebrating ten years in the Premier League.
He told the Daily Star Sunday: "No, Wayne won't look at Van Persie as a threat. He will look at his signing as a spur. This will kick Wayne on to even more greatness.
"Van Persie coming in will excite him. After listening to what people have been saying about Wayne, I think he's thirty-two because they're talking about him as if he's finished.
"He's twenty-six and he's not hit his prime yet. He's got his best years ahead of him - and he knows that.
"He's got the challenge now and it could be the best thing that's ever happened to him."
The Alan Stubbs Everyman Cancer Appeal was launched to raise awareness of testicular cancer, which he suffered and fought back from.