The Netherlands international has started just two Premier League games since joining United from Ajax in a £40m deal last summer.
Solskjaer revealed at the weekend that Van de Beek is not happy with his situation, not helped by being hauled off on a rare start against Liverpool in the FA Cup on Sunday.
However, The Athletic claims that Solskjaer has held face-to-face talks with the Dutchman and informed him that he will now start more regularly.
A number of clubs are believed to have made a loan approach for the 23-year-old, but United are said to have ruled out a short-term departure.
Van de Beek scored his only goal of the season against Crystal Palace on his United debut back in September.