Mata reacted angrily to being substituted in Wednesday's Premier League win at Southampton and afterwards Mourinho suggested the "door is open" should Chelsea's player of the year for the past two seasons wish to leave.
There have been reports of interest from the likes of Paris St Germain, Napoli, Inter Milan and Manchester United in Mata, but Mourinho insisted no offers have been received and praised the World Cup winner's performance in training ahead of Sunday's FA Cup third-round clash at Derby.
"I keep saying that I want him to stay," Mourinho said.
"There isn't offers. We have no offers. When I said 'I don't want him to leave', he was focused on that and not focused on when I said 'the door is always open'.
"Today (Friday) he trained in a fantastic way, so no problems."
Belgium forward Kevin De Bruyne has also been linked with a move after being frustrated by a lack of opportunities this term, following loan spells in the first 18 months of his Blues career.
"We know that he fancies a move but he is a fantastic player and fantastic players are very expensive," Mourinho said.
"I don't want him to leave but we have a couple of contacts, made not by us because we don't want to sell.
"We know that Kevin didn't adapt very well to the difficult life a Chelsea player has.
"(He was a) very important player for Genk, very important player for Werder Bremen. It's the first time he comes to a big club with big competition. They have to accept this competitiveness."
Mourinho has warned any players wanting out, and any clubs pursuing them, that they will not be leaving on the cheap.
He added: "If people think they can get our good players on sale, sales finished in London yesterday (Thursday)."
Mourinho says he makes decisions in a pragmatic way, putting the team first.
"When I have to make decisions I always try to be a cold one, icy, analyse the situation and try to make the best decision for the team and put the persons (involved) in the second level," he said.
Chelsea have been linked with purchases this month, particularly a striker.
Mourinho quashed reports of a £50million offer for Napoli's Argentina striker Gonzalo Higuain, who played under him at Real Madrid, and insisted the Blues will not be signing a striker this month.
Mourinho said: "Nothing is true about Gonzalo. He's a player that I know we cannot get. He's a player that moved from Real to Napoli six months ago, he's doing very well, he's adapting very well to Italy.
"I don't believe they're interested in selling Higuain, so why should we be interested in somebody we feel is impossible to come?"