Mourinho has landed European football's biggest prize on two previous occasions with Porto and Inter Milan.
He was, however, unable to guide the Blues past the semi-final stage during his first spell in charge at Stamford Bridge and was watching from afar as Roman Abramovich's dream was finally realised by Roberto Di Matteo in 2012.
Mourinho concedes that he is hoping to "build a dynasty" after returning to the Chelsea hot-seat, but insists no emphasis is being placed on the need to be successful in continental competition.
Ahead of a Group E opener against Basel on Wednesday, he said: "Let's see what happens. I have to focus not on the past but on the future.
"There's no obsession for me with this competition. No obsession for Chelsea. But I want to win it for a third time, and I want Chelsea to win it for a second time.
"This is the beginning of a process with us and the Champions League.
"We made history by winning it two seasons ago. Last year we made history by being the only champions eliminated from the group stage after six matches, and we ended up in a competition we didn't want to play in.
"This season we have some players with different experience, but the potential to win it.
"We have to build a team full of talented players without the experience and the football philosophy born of having worked together for a long time.
"The process has to end with a team, a philosophy, an identity, a style of play.
"If we win a match but not in the style we're trying to build, it's three points, one step up the table but one step back in the direction of our work. What we want to do is both things at the same time.
"If we'd gone to Everton (on Saturday), had a very bad match and, in the last minute, Leighton Baines had scored an own goal and we'd won 1-0, would we be happy? In normal circumstances, yes, but when you're trying to build something different? No."