Mourinho is to leave Real Madrid at the end of the Spanish league season and is expected to return to Stamford Bridge, where the managerial post is vacant following the end of Rafa Benitez's interim spell in charge.
Mata arrived at the club after Mourinho's departure but is well aware of everything the Portuguese has achieved and would be happy to see him handed the reins.
"Jose is one of the best," Mata said. "He won everything in every country he was - in Portugal, in Italy, in London with Chelsea, and in Spain as well.
"We don't know really what is going to happen but if he comes he is welcome because he is one of the best and Chelsea always want to be a top side.
"If he comes we are going to be happy to have him."
Mourinho has faced criticism during his time at Real Madrid and will finish this season without a major trophy, but Mata believes he could help Chelsea challenge for major honours next year.
He said: "What I know is that Madrid is a massive club with a lot of pressure on them, and it shouldn't be easy to be manager of Real Madrid.
"If he comes we will try and do our best with him, or whoever, to win the title, because one challenge for me will be to win the Premier League."