The England international scored twice against Norwich City to ensure Giggs's reign as manager got off to a winning start, as United eased to a 4-0 victory at Old Trafford.
"It was a bit strange [playing under Giggs]," Rooney told Sky Sports following the game. "I've played with him for the last 10 years but we all know Giggs is a really experienced player and has been part of the coaching staff for the last season.
"He's built to be a manager. Us as a team, we can see that. We can see by the way he's handled himself since he's took over. It was fantastic to get out there and get the win for him.
"I think Giggsy's got all the credentials to be the next boss but that's down to the board. Who knows?"
United remain in seventh place in the Premier League table following the victory.