Mourinho left the door open over a potential departure in the January transfer window after Chelsea's impressive 3-0 win at Southampton on Wednesday.
Mata – who has been out of favour with Mourinho despite being the club's player of the year in each of the past two seasons – showed his frustration when substituted in the 53rd minute for Oscar.
Brazilian Oscar and fellow substitute Willian helped swing the match Chelsea's way though, as both players, and Fernando Torres, scored in the last 30 minutes at St Mary's Stadium.
The Chelsea boss said he was not aware of Mata's reaction to being substituted but added that he would like to keep him at Stamford Bridge.
"I don't want him to go, that is my opinion and that is my wish – but my door is open," he said.
"The club door is open too, so when a player wants to speak with us we are there waiting for them.
"But if you ask me do I want to sell him, I don't want to. I didn't see the reaction, his frustration was because of the result – we have to win.
"If we don't win this game then the difference to the leaders is bigger. At the end of the game, everyone including him was celebrating the victory."
Mata was linked with a switch to Manchester United last year, and has seen Oscar move ahead of him in the pecking order as Chelsea's primary playmaker this season.
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
