The Sun says England's goal hero against Sweden is waiting to see if Van Persie can be persuaded to stay before committing himself.
Juventus are ready to make a huge pre-contract offer in January if Walcott does not sign.
Dutch hero Van Persie also has just a year to run.
If he decides against a new deal, then Walcott is prepared to sit tight and let Europe's elite come to him in the winter transfer window.
A source said: "It seems unbelievable the club has left it until well into the last year of the contracts and still not managed to get either player sorted."