Mata endured a frustrating 2020-21 campaign, making just 10 starts and eight substitute appearances in all competitions.
While just three of those starts came after the turn of the year, there have been suggestions that the 33-year-old is open to extending his stay at the club.
The Spaniard is currently free to speak to other clubs with his contract due to expire at the end of the month.
The report adds that Solskjaer would like to keep Mata, who would also need to accept a one-year contract to stay at the North-West giants. body check tags ::