The 24-year-old arrived at Old Trafford from Ajax last September and has made 33 appearances for the Red Devils during the 2020-21 campaign.
The Netherlands international has only contributed one goal and two assists for Ole Gunnar Solskjaer's side, though, and he is down the pecking order when it comes to the midfield positions.
A recent report claimed that Man United were not prepared to entertain any offers for the Dutchman in the upcoming market.
However, according to Calciomercato, Mourinho is determined to sign the midfielder for his new club and hopes that a deal can be completed for a fee in the region of £26m.
The former Tottenham Hotspur manager has also been linked with Van de Beek's teammates Juan Mata and David de Gea since it was confirmed that he would take charge of Roma next term.