Some are expecting a title challenge from Louis van Gaal's side next season, but Sheringham says it will be difficult.
Despite a poor start to the 2014/15 campaign, United rallied in the second half of the season to finish fourth and secure a return to the Champions League at the first time of asking.
That was arguably the job manager Louis van Gaal was brought in to do, although their form in the second half of the year has some suggesting that a Premier League title challenge could be on the cards next term .
Sheringham, though, doesn’t agree, saying it would take an extraordinary effort for the Red Devils to overhaul defending champions Chelsea and local rivals City.
"When clubs finish so far off the championship winners it’s very difficult in the next season. They’ll have to be extra special to beat Chelsea or Manchester City next year, obviously that’s the aim. I don’t think it’s as easy as said than done.”
Improvement needed up front to catch up
If there is one area that United are currently lacking in compared to their rivals, it is up front.
Both Chelsea and Manchester City have prolific goalscorers to lead their attacks, with Sergio Aguero having been consistent in the Premier League for a number of years and Diego Costa impressing during his first campaign in England last year.
In contrast, Van Gaal currently has Wayne Rooney as his best forward, with the likes of Robin van Persie and Radamel Falcao both failing to make the grade last season.
An addition of a top forward should be a priority then, with reinforcement in that area of the squad likely to help them in the their efforts to bridge the gap between themselves and the current top two.