The Portuguese manager has bolstered his side's ranks this summer by signing Andre Schurrle, Marco van Ginkel and Mark Schwarzer, along with the return of Romelu Lukaku after a loan spell at West Bromwich Albion.
Mourinho told the club's official website: "We have two players for each position and the competition will be high but we hope Chelsea can go all the way in every competition.
"We hope to arrive in the later stages of the cups too. So with 60 matches we need all of them."
Chelsea beat AC Milan 2-0 in their pre-season friendly clash on Sunday, thanks to strikes from Kevin De Bruyne and Andre Schurrle.