Since Roman Abramovich bought the west London club in 2003, the Russian has pumped huge amounts of money into it in order to try and win Europe's top competition.
The Blues did manage to reach their first Champions League final in 2008, only to lose on penalties to Manchester United, with then-manager Avram Grant being removed soon after.
|VAN DER SAR BACKING BLUES
|The former Manchester United goalkeeper believes Chelsea can beat Bayern
The 24-year-old Mata, who was signed from Valencia in the summer, revealed that the squad want to make history by defeating Bayern Munich, while adding that it is also important to qualify for next season's tournament.
The Spaniard told Press Association Sport: "We want to win for the club, and for us, because we can make history for Chelsea.
"But, as well, it's important to play in the Champions League next year. Chelsea always want to be in the Champions League."
Winning the final, which is to be staged at Bayern's home ground the Allianz Arena, is now the only way the Premier League side can cement Champions League football for the 2012-13 season, after a disappointing league campaign.
However, the £23 million man insisted that if they triumph in Germany, adding to the FA Cup victory against Liverpool, the season will have been a success.
"It hasn't been an easy season for us in the Premier League," Mata continued.
"We are in sixth position, so it's not what Chelsea deserves. But we won the FA Cup, we have the chance now to win the Champions League as well. So, if we win both, it will be an amazing season for us."
Nevertheless, there is still much speculation concerning Di Matteo's future at the club.
|KINGS OF EUROPE?
|4.25||Chelsea can be backed at 4.25 to win the Champions League with 188BET|
Mata was signed by former Blues' boss Villas-Boas but gave his support to the interim boss. However, he would not say whether he thought the club's former midfielder Di Matteo would get the job permanently.
"Robbie's a very good guy, a very good person," the midfielder said of Di Matteo. "He has character, he knows Chelsea. He used to play [for the club], now he's training. So he's a very good manager and we are all with him.
"We don't know, we don't know [whether he will get the full-time role]. It's not our job. But I think all of us are happy with him. We have to win the final of the Champions League and now that's it."
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.