Mata's Red Devils deal is closed at the end of the season and has not offered a new deal.
This means that the Spaniard can start talking to foreign clubs about a possible pre-contract contract that would bring him in the summer.
Mata was not used by Ole Gunnar. Solskjaer has felt very good since his arrival in Norway.
The former Chelsea man is happy to stay with United, but is still waiting for a new offer from United bosses.
And the metro Allegation that Solskjaer asked Mata to stay at Old Trafford.
Mata is represented by his father, who is reportedly meeting for tough talks at the Carrington training ground to iron out the situation.
United States legend Gary Neville commented on the players who will not have much playing time under Solskjaer after defeating Tottenham on Sunday at Wembley.
Mata, who joined Chelsea United in January 2015 for a fee of £ 37.1 million, was one of them.
"Over the weeks, you've seen more of his impact on the team in terms of the attacking game and the forward runs," he said.
"The profile of the team has changed. During the commentary, we talked about Marouane Fellaini, Juan Mata and Romelu Lukaku leaving the starting eleven.
"I said a few years ago on Monday night football when Mata was signed that he was a wonderful player, but I thought it was a violation of philosophy.
"I did not think he fit into the profile of a Manchester United player."
Mata's has always been known as one of football's nice guys and is a popular member of the locker room at Old Trafford.
United, like Chelsea, has often offered shorter contracts to players over the age of 30.
United has an FA Cup match against Arsenal towards the end of the month. This is a game Mata could offer for starters to get a rest.
The 30-year-old has scored 50 goals in the Premier League since signing for Chelsea in 2011 in Valencia.
He has also recorded 50 assists and won two FA Cups and a League Cup in England.
His biggest club success, however, will no doubt be when he won the Champions League in 2012 with Chelsea.
The former Valencian won with Spain the World Cup and the Euro-World Cup and scored in 2012 the final of the latter.