United are currently fifth in the Premier League and are just three points off fourth-placed Chelsea. However, the Red Devils were on an 11-game undefeated streak when football was suspended.
Solskjaer has backed himself in building a youthful side, with the likes of Marcus Rashford, Anthony Martial, Mason Greenwood, Daniel James, Arron Wan-Bissaka and Scott McTominay.
And Hargreaves, who won a Premier League title and the Champions League during his time at Old Trafford, believes Sancho will want to be part of this project.
“Often you see a lot of teams sign players and sometimes you think ‘that’s not a good fit’,” the BT Sport pundit said.
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Sancho made an 11-minute appearance off the bench as Dortmund beat Schalke 4-0 on Saturday as the Bundesliga resumed playing matches.
The England international is having a great season for Dortmund and so far this season he has scored 17 goals and has provided 19 assists in 36 appearances in all competitions.
However, he is under contract with Dortmund until 2022 and the German club are seeking a fee of around £100million to consider selling him.
And while Hargreaves thinks this is a lot of money, given the state of the current market, he thinks United will be looking at the player as a long-term investment.