Dutch manager Louis van Gaal has been tasked with returning United to the summit in 2014-15 after a forgettable season under David Moyes and confidence is high following the club's unbeaten pre-season.
United won all five games on their tour of the United States, while they edged Valencia at Old Trafford in midweek.
But having failed to add to the early arrivals of Luke Shaw and Ander Herrera, Scholes - an 11-time Premier League winner at Old Trafford - said United were lacking in key areas to challenge for the title.
"I think the title is between City and Chelsea, they've both made decent signings. The next two places are between United, Liverpool and Arsenal," the 39-year-old said.
"United will be looking for a better season than last season, and that shouldn't be too difficult. It was a big blip last year. Disappointing.
"I'm sure he [Van Gaal] would have liked to have signed more players. He's not managed to do that yet. Are the players out there available? The areas they need, in midfield, is an area where I thought they might have bought a couple of players.
"It's not because they're not in the Champions League [that players aren't joining United]. Maybe if they were out of it for three or four years, but United is such a massive club. Being out of the Champions League will hopefully only be for one year.
"The chance to win the Premier League... possibly not this year if they don't make any more signings, but they'll definitely have a better year than last year. Confidence was low at the start of this season and I think this manager has brought that back."
United open the season at home to Swansea City on Saturday, which is followed by fixtures against Sunderland, Burnley, QPR, Leicester City and West Ham.
"The first six games look favourable and if they can be near or top of the league at the end of those six then take it from there," said Scholes.
"I just worry that City and Chelsea have a bit too much for them."
