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.