Rooney was left out of Gareth Southgate’s squad for Wednesday’s 1-0 friendly defeat to Germany and Sunday’s World Cup qualifier against Lithuania, having been battling a knee injury while the England boss also had doubts over his lack of game time.
Rooney has made only nine Premier League starts for Manchester United this season and scored just five club goals with his future at Old Trafford in doubt.
But Southgate has said record England scorer Rooney, who has 119 caps, remains in his thoughts and Scholes feels he should stay as part of the squad.
“Wayne has been a sensational footballer for England and Manchester United for nearly 15 years. He is greatly respected and I still think he has a part to play with United and England,” he told BBC Radio Five Live’s Sportsweek.
“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.”
England are top of Group F by two points ahead of facing Lithuania at Wembley as they aim to qualify for next year’s World Cup in Russia.
It will be Southgate’s first competitive match since he was appointed full-time boss in November and Scholes believes the ex-Middlesbrough manager deserves time despite a lack of success in club management.
“As an England manager you’d probably like to earn your stripes, I don’t think he’s done that on the European stage or the domestic stage with club management,” he said.
“He did great with the [England] under-21s but we’ve been down every other route, down the route with so-called super coaches and it hasn’t worked. Now we have a passionate man in charge.”
