Greenwood is currently on loan at Getafe and was watched by Mitchell during his team's La Liga win over Cadiz on Monday, according to Mundo Deportivo.
The forward played 86 minutes of the match and grabbed an assist for Borja Mayoral's winning goal.
Greenwood has now made eight La Liga appearances this season, scoring once and providing two assists. The 22-year-old also bagged a brace in a 12-0 Copa del Rey win over Tardienta.
Manchester United chief executive Richard Arnold has said there is "no expectation" of Greenwood playing for the club again but changes are expected to be made at the club after Sir Jim Ratcliffe takes up his 25 percent stake.
Arnold and director of football John Murtough could leave the club, with Manchester United reportedly "close" to reaching an agreement for Mitchell to come in and work as the new sporting director.
Ratcliffe wants to overhaul the club's transfer strategy and is also hoping to offload players such as Jadon Sancho, Antony and Anthony Martial in the January transfer window.
Meanwhile, Greenwood is thought to be loving life in Spain and is keen to continue in La Liga. Sevilla and several other Spanish sides have already been linked with a move for the youngster.