Mourinho's long-awaited return to Stamford Bridge was confirmed on Monday when he signed a four-year contract to replace interim manager Rafael Benitez.
Chelsea have won the league just once since Mourinho led them to successive titles in 2005 and 2006.
Mata has enjoyed success in Europe with Chelsea, winning the Europa League this summer 12 months after the team's success in the Champions League.
Other than the League Cup, the only domestic trophy the Spaniard is yet to win is the Premier League and he wants that to change next year.
"Winning the Champions League, FA Cup and Europa League was great, but I really want to win the Premier League title next season," the Spaniard told Chelsea's website.
"If we start well I think we can do it. We have a great squad and fantastic supporters behind us, so hopefully we can do it.
"For me it would be amazing to win four trophies in three seasons. It would be a very special feeling to win the Premier League title and I'm looking forward to hopefully doing so."
Mourinho underlined his desire to keep David Luiz at Chelsea in his first interview since taking over, and he also spoke about the need to strengthen the Blues squad.
Chelsea are in talks with Bayer Leverkusen over the possible signing of forward Andre Schurrle.
Mourinho met with Leverkusen general manager Rudi Voller prior to Michael Ballack's testimonial in Leipzig, where the Portuguese managed a World XI in the German's final match before retiring.
Several other targets have been mooted, including Zenit St Petersburg striker Hulk and Fiorentina forward Stevan Jovetic.
There are likely to be several outgoings this summer too. Florent Malouda has already admitted he will leave while Hilario, Ross Turnbull, Paulo Ferreira and Yossi Benayoun are also out of contract.
Benayoun has been linked with a move to the United States, but the Israeli's agent Ronen Katzav says the 33-year-old midfielder has other options too.
He said on Thursday: "He has several offers - not just from America, but Italy, England and Germany too.
"We are talking about what to do next, but it's too early to say which is the best option yet."
Turnbull has been unable to edge Petr Cech out of the Chelsea team since moving to Stamford Bridge four years ago.
The 28-year-old, who made just six Premier League starts during his spell at Stamford Bridge, is understood to be in talks with four English clubs.