Mata was taken off after playing just 30 minutes of football during United’s win over Leicester City in the Community shield last weekend, sparking speculation about his future.
TalkSport claimed that Mata handed in his transfer request after the incident in what was described as being the final straw.
However, Mourinho denied claims that Mata was unhappy with the decision in his pre-match press conference ahead of the Bournemouth game.
“He was very happy that he was my first choice to come on to the pitch in a difficult moment of the game for us after we conceded a goal,” Mourinho was quoted as saying by the Express.
“At that moment Mata was the first player to be called up to play and played 25 minutes.
“He was really happy with his contribution.”
Fenerbahce are reported to be interested in Mata according to TalkSport who claim the 28-year-old is valued as being worth £20 million.
Mata and Mourinho have a frosty relationship after the Portuguese manager got rid of him during his time in charge of Chelsea – ironically he was sold to United.
The Super Lig giants are in pursuit of a new attacking midfielder after parting ways with Diego Ribas and Luis Nani over the summer transfer window.