Mourinho feels the addition of Diego Costa and Cesc Fabregas to the squad has boosted his options but feels as many as six teams could realistically challenge for Premier League glory.
Chelsea begin their season away to Burnley – live on Monday Night Football – and Mourinho is expecting a tough test, both at Turf Moor and throughout the season.
“We bought some key players and we feel these players have brought the squad into another dimension,” he said.
“We are title contenders but if you are expecting me to say we are going to win the Premier League, I cannot say this.
“I have to respect this competition and in terms of country’s championships, this is the only one with more than two contenders. There are five or six.
“I want to win against Burnley - that is the first step. To win against Burnley will be very hard.”
Mourinho must choose whether to keep faith with Petr Cech in goal or give the highly-rated Thibaut Courtois his opportunity to establish himself after impressing while on loan with Atletico Madrid.
“With all respect to the fantastic goalkeepers around the world, I think Chelsea have two of the three best goalkeepers in the world,” he added.
“This is something unique. I cannot kill competition, I cannot close the door for someone to get into the team
"And I cannot give a player, even a goalkeeper, guarantees that he is my first choice forever, if he doesn't perform.
"Obviously you cannot change a goalkeeper if he makes a mistake, but you can change a goalkeeper if he makes five mistakes.
"And so what is my first choice today cannot be my first choice tomorrow, it depends on performance. But if the goalkeeper gives stability to the team then I don't see a reason to change.
"I don't do, 'You are the keeper in this competition, you are the keeper in that competition'. I must support the keeper who is not first choice, and to support him is not to give him a Capital One Cup game. Supporting him is showing him my trust: when nobody is expecting."
Watch Burnley v Chelsea on Monday Night Football. Coverage begins on Sky Sports 1 at 7pm.