The Premier League champions face the FA Cup winners in the Community Shield, with Mourinho refusing to discuss the Blues' bid to prise defender John Stones from Everton.
The Chelsea boss is short of options in defence, but is optimistic about his strikeforce, which has seen Radamel Falcao come in despite a below-par season on loan at Manchester United from Monaco last term.
Diego Costa was a key addition ahead of Chelsea's title-winning season, but cover was lacking when the Spain striker's fragile hamstrings flared up.
Costa is fit for Wembley despite withdrawing from the pre-season clash with Barcelona in the United States.
Mourinho said: "I believe (Costa is free of injury), but I'm not worried about it
I go match after match.
"Three top strikers
If one is injured we have two
No concerns, no protections
It's a position where we're very strong."
Mourinho was asked three questions on Stones: for an update on Chelsea's pursuit of the England defender, whether a new bid had been rejected by Everton and whether Chelsea expect to go in for him again
Each time he replied "no".
"I don't speak about players from other clubs, especially now competition starts," the Portuguese added.
"It starts for us and Arsenal now and next week starts for everyone
It's enough for me."
Chelsea are trying to sign a left-back as they have only Cesar Azpilicueta following Filipe Luis' return to Atletico Madrid.
But Mourinho would not be drawn on a move for Ausberg's Baba Rahman.
Falcao and goalkeeper Asmir Begovic are Chelsea's only summer captures at first-team level, the latter a replacement for Petr Cech.
Cech left for Arsenal after 11 years after falling behind Thibaut Courtois in the pecking order in a move sanctioned by Chelsea owner Roman Abramovich.
Asked about facing Cech, Mourinho said: "I did it already
Inter against Chelsea
No problem."
It has been argued Cech has filled a problem position for the Gunners.
"I don't agree with you," Mourinho added.
"I never felt weaknesses in their keepers."
Mourinho has not lost in 13 matches as Chelsea manager against Arsene Wenger's Arsenal.
Mourinho again played down the personal record, saying: "Doesn't matter Arsenal, doesn't matter the manager
"I just want my teams, my clubs to try to get the best possible results
That's the only thing that matters.
"In football you can win or lose or draw
In this case you have to be ready for everything.
"I never made my victories over Arsenal an explosion of happiness or special pride
I will not make a drama if one day we lose.
"(But) we always try to play for a result and Community Shield has a motivation, obviously different than just a friendly or just a summer tournament
I would say it's the start of the competition."
Mourinho has a full squad to select from, with defender Gary Cahill also available despite a blow to the nose against Barca.
Source : PA
Source: PA