The London clubs have shown an interest in signing the 27-year-old striker this summer, who asked to leave the club at the end of last season - according to Sir Alex Ferguson.
But Scholes, who retired from football for a second time in May, is convinced that Rooney would be best served by staying with the Premier League champions.
|MANCHESTER UNITED LATEST
|20/1||Wayne Rooney is 20/1 with BetVictor to be the Premier League's top scorer
“It's up to Wayne - but he's a top, top player and every player and fan wants him to stay.”
New United boss David Moyes has yet to make any significant moves in the transfer market, with Barcelona adamant that target Cesc Fabregas is not for sale, but Scholes does not believe the Scot is under pressure to recruit.
“I don't think there's that much pressure,” the former midfielder continued. “He's got a quality squad there, with already 18-20 quality players
“Even if Sir Alex Ferguson was there he would want to sign two or three players. That's the norm every season - to improve the year after, even if you've won the league.
“I'm sure David Moyes is trying to get players - and hopefully he'll get the ones he wants.”