The Red Devils currently sit fifth, four points behind fourth-placed Liverpool but with two games in hand.
However, while United still have to play four of the other five members of the top six, their great rivals from Merseyside have a relatively straight-forward run-in.
After Saturday’s derby against Everton, the remainder of Liverpool’s Premier League fixtures are against teams placed eighth or lower.
Scholes is confident United will finish in the Champions League qualification spots but admits the away games against Manchester City, Arsenal and Tottenham will be crucial.
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“The chances are good and I expect them to finish fourth. They have been on a fantastic run, without making much progress in the league,” Scholes said of United, who haven’t lost in the top flight since October.
“I think [United’s season] has been alright. There is a big period now, this will define how good the season has been.
“They have got three tough away games. If they can get through that with five or six points, they have got a great chance of finishing in the top four.”
Scholes is also upbeat about United’s chances of winning the Europa League and believes there is only one team capable of stopping them in their tracks.
“It is a great chance for them,” Scholes told Omnisport . “They are obviously the biggest club left in the competition. They are favourites and rightly so.
“If they perform anything like [they can] they have got a great chance of winning. I think Lyon are maybe the obvious contenders to United. But, apart from that, I don’t see too many problems for them in that competition.”