The Spaniard has fallen behind Brazilian Oscar in the pecking order since Mourinho's return to Stamford Bridge in the summer, despite being the club's player of the year last season.
Mourinho has told the 25-year-old he must fit in more with his style, work on his defensive play and become more consistent.
And Mata has vowed to do whatever it takes.
"I will play wherever he demands," Mata told the Sun. "I am young and can still improve. I want to do the same as I did in the last two seasons.
"My dad always said if you are left-footed improve with your right.
"I have to improve defensively, too. Every single player has to. To be the perfect player is very difficult but I have tried throughout my career to improve a lot."
Mourinho pronounced himself pleased with Mata's efforts in this week's Capital One Cup win over Swindon, praising his attitude and effort.
Mata said: "I think Jose can help me. Every manager can try to improve their players. It's his job to bring the best out of his players.
"Last season was the best in my career, but I could still have done better.
"Jose's a manager who analyses everything, not just in our team. He's a manager who likes intensity, who likes pressure. We have eight months to go to the World Cup and I believe in myself more than ever."
I firmly agree with this...... Jose is challenging him and will make him even better. The premier league should watch out the messiah will be reborn- stamford10