The Red Devils get their campaign underway later today when they welcome Swansea City to Old Trafford.
Despite increased optimism around the club following the appointment of Louis van Gaal as manager, Scholes believes that United will fall short when it comes to the title race this term.
"Louis van Gaal is a top manager - as he's let everyone know, he's won the league in every country he's been in, so we're just hoping he's going to get this team better than they were last year and we're ready to challenge for the league," he told BT Sport.
"I don't think it'll be this year but I think he'll make them better. I just think Chelsea and Man City have better squads. To go from seventh to winning the league is a massive ask."
United head into the new Premier League campaign on the back of six consecutive wins in pre-season.