The 20-times English champions slumped to seventh last season during the short reign of David Moyes, but even with seasoned title winner Louis van Gaal in the Old Trafford hot seat, Scholes is not expecting a title challenge.
"I think the title is between City and Chelsea, they've both made decent signings," Scholes said in Friday's Daily Mirror on the eve of the new Premier League season.
"The next two places are between United, Liverpool and Arsenal. United will be looking for a better season than the last and that shouldn't be too difficult.
"I'm sure Van Gaal would have liked to have signed more players. Midfield is where I thought they might have brought in a couple."
United, who start with a home match against Swansea City on Saturday, have signed midfielder Ander Herrera from Athletic Bilbao and full back Luke Shaw from Southampton but have lost the likes of Nemanja Vidic, Rio Ferdinand and Patrice Evra.
While Van Gaal still has time to strengthen the squad, Scholes is surprised United have not been more active.
"(Toni) Kroos goes for 20 million and (Cesc) Fabregas to Chelsea. I thought they would have been in for those type of players but it doesn't look like they were.
"Remember the players they have lost - Rio, Vidic, Evra, Giggs. Massive playrs who have won 30 titles between them.
"It's only Shaw and Herrera who have come in and (Juan) Mata and (Marouane) Fellaini who haven't won the league. I just worry that City and Chelsea have a bit too much for them."
Scholes remains optimistic though that Van Gaal, who he describes as a "mad genius" will begin the process of returning United back towards the summit.
"From what I've seen in pre-season he looks a bit mad - a bit like a mad genius," Scholes said of the former Ajax, Barcelona, Bayern Munich and Netherlands coach.
"I think he's brought a bit of fear into the players, which is no bad thing. I played for 20 years under Alex Ferguson and he could be a scary man. Sometimes fear can bring performances out of you. There's no doubt these players need to perform.
"If not I don't think they will be there very long."
(Reporting by Martyn Herman; editing by Sudipto Ganguly)
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