Southgate voiced his concerns over Rooney's knee injury as to why he was left out of the England squad.
The Three Lions boss admitted yesterday that Rooney is still very much in his thinking for their World Cup qualifying campaign.
Wayne Rooney has been linked with a move away from Old Trafford this summer
Paul Scholes doesn't want Rooney joining another Premier League club
And Scholes believes Rooney will relish the challenge to rediscover his form for club and country.
"Wayne has been a sensational footballer for England and Manchester United for nearly 15 years," Scholes said.
"He is greatly respected and I still think he has a part to play with United and England," he said.
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Rooney was dropped from the England squad by Gareth Southgate
"He has great experience, he can pass knowledge on to young players and it's up to Gareth if and when he wants to use it.
"I don't want to talk about him going to another English club, I hope he gets himself back into the United team. He has a fight on his hands but the Wayne Rooney I know is someone who will face that challenge and try to do it.
"He still has a prominent role to play for England and United. There's been a lot of speculation over where he goes now but Wayne, with what he's done, has earned the right to do what he wants to do. I hope he does stay and fight."