The former Barcelona midfielder had spent most of previous day in meetings with club officials
Allardyce was appointed England manager on Friday on a two-year contract, replacing Roy Hodgson, who quit following the team's last-16 exit from Euro 2016 at the hands of Iceland.
"I think it's a good appointment," Rooney, who is in China as part of Manchester United's pre-season tour, told reporters.
"He will probably bring a different way of playing to England. Hopefully it's a good way and we can be successful under him."
The England skipper, who is also his country's highest goalscorer, said he had no intention of retiring from international duty.
"Am I going to carry on? It was asked of me after the Euros, but yes, I'll be there," the 30-year-old added.