Mata has long been linked with a move away from Stamford Bridge and reacted furiously to being substituted in Chelsea's win over Southampton.
"I want to keep him. I don't want him to go. That is my opinion, my wish, but my door is open," Mourinho said.
"The club's door is open too so when a player wants to speak to us we are there waiting for them.
"If you are asking do you want the club to sell him? I don't want to."
Essien is reportedly considering leaving Chelsea due to a lack of playing time.
"I offer nobody - not Michael, not nobody (guaranteed playing time)," the Portuguese said.
"I understand that players think about national team, the World Cup and playing regularly, but my players have to think of the team before the players. Michael knows that perfectly."