Rooney said he has “no doubts” that Rosenior could do a good job for Chelsea.
Enzo Maresca left his role at the Blues after 18 months in charge, having fallen out with the club’s owners.
The last time Rosenior worked in the Premier League was as a player for Brighton in 2017.
As a right-back, he had a solid but unspectacular career as a player – also featuring in the top flight for Fulham, Reading and Hull.
Roughly half his career was spent in the EFL and that is where he started his coaching career.
After a spell as Brighton‘s under-23s coach, he spent three years at Derby – working with Phillip Cocu before Rooney.
“He’s also got a side which you don’t want to cross him as well,” said Rooney.
“That’s important as well. If he goes in there, he won’t disappoint. He’s been waiting for an opportunity like this.
“If you don’t take it now, then you’re never going to take it. And I think he’s done his apprenticeship, he’s done his work to try and get to that job.
“So he’ll have no doubts in his mind that he’s capable of doing that job. And hopefully, very soon, hopefully we hear that he is the manager, because for young English coaches I think it’s massive.
“We don’t really see English managers at big clubs. So he’d be leading the way for for us.”
The only English managers currently in the Premier League are Newcastle‘s Eddie Howe, Burnley‘s Scott Parker and Nottingham Forest‘s Sean Dyche.