Rooney captained the Three Lions for the first time in a competitive match on Friday, scoring twice as England swept aside San Marino 5-0 at Wembley.
He told The Sun: "I can see Wayne being promoted to England captain full-time one day.
"I think his performance was a touch enhanced by being handed the skipper's armband. Perhaps that little bit of extra responsibility had an effect on him."
Liverpool midfielder Gerrard will take the armband back this week as England continue their World Cup qualifying campaign against Poland on Tuesday, with Rooney reverting to a vice-captain role.