The Dutchman struggled for regular football at United last season.
Signed as an alternative to Bruno Fernandes, van de Beek struggled for minutes in the Premier League and was restricted to the odd start in cup matches.
Asked about van de Beek during a preseason interview, manager Solskjaer hinted the Dutchman would be around in the coming season.
He told MUTV: "You've not experienced Manchester United until you've scored in front of the Stretford End.
"Of course, Edi [Cavani] scored in front of some of them, and they've both scored in that end, but now, when it's a full stadium, it will be different for the two of them.
"Manchester United with and without fans are two different things. To be reunited with them will be top."
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