Mourinho has preferred to deploy Spain right-back Cesar Azpilicueta on his 'wrong' flank rather than select Cole, who is short of full fitness due to a niggling rib problem which forced him out of England's friendly defeat to Germany.
Cole, 33 next month, is in the final year of his Blues contract, but has not been told to buck up his ideas.
"Ashley is a top professional," Mourinho said.
"He just needs time to recover 100% and put himself at the top of his game and to fight to have his position.
"He's not the kind of personality you need to leave on the bench to send him a message to him to make him realise that he has to give more. No way."
With Mourinho apparently less than impressed by Ryan Bertrand, whose favoured position is on the left of defence, Azpilicueta is likely to keep his place against West Ham on Saturday, despite Cole returning to the squad.
"I don't have a dilemma," Mourinho said. "I play Azpilicueta because he's stronger at this moment. He's physically at the top of his game. He's strong.
"(Cole) is not injured. He feels pain. He has not a broken rib any more. He is in condition to play football.
"He has a little bit of pain. It's a limitation. Can he sprint 100%? Maybe not. Can he jump 100%? Maybe not. But he's not injured."
Mourinho likened the situation to other sportspeople who perform with injuries and may have been referring to Rafael Nadal, who was at Stamford Bridge at the start of November while playing in the ATP Tour finals at the 02, when he made reference to a tennis player.
"I was speaking a few weeks ago to a top tennis player and he told me it's very rare he plays a game 100%," Mourinho added.
"He always has something: one day a finger, another day the back, another the ankle. He's almost never feeling absolutely top.
"It's the same for football players. He (Cole) has pain at this moment.
"He coped with it at a certain level. He's ready to go and to play. But he has a little limitation."
Like Cole, John Terry and Frank Lampard are in the final years of their contracts, while Mourinho has decisions to make in the generation game, including at goalkeeper.
Mourinho repeated his belief that he has the world's number one goalkeeper at his disposal in Petr Cech and the world's best young goalkeeper on Chelsea's books, too, in Thibaut Courtois.
The Belgium goalkeeper, who has two years left on his Chelsea contract following his 2011 move from Genk, is on a third season-long loan spell at Atletico Madrid and has been linked with Barcelona, among others.
Chelsea hold all the cards in that situation, Mourinho said.
He added: "We are in control of the situation. Anything that can happen in the future depends on Chelsea FC."
Brazil midfielder Ramires has also been linked with Barcelona, a prospect Mourinho dismissed.
"There is no price for Ramires in the market," Mourinho said.
"(The interest) doesn't annoy me but, on behalf of Chelsea, there's no price for a club wanting to buy Ramires.
"If it's true or not, it's not important. There's no price."
West Ham were likened to Barcelona following their 3-0 win at Tottenham in which they operated without a striker.
Mourinho conceded the Hammers were "positionally" similar to the Catalans on that occasion, before suggesting he is ready for whatever approach Sam Allardyce opts for at Upton Park.
The Portuguese said: "I'm prepared for the two situations: for them to play with, for example, Carlton Cole as a target-man, or without that targe-tman and with (Kevin) Nolan or somebody else coming from midfield. It will be difficult both ways. Different, but difficult."
It is the start of a key period, with fixtures coming thick and fast and no pause for international breaks.
"Many things are decided in these three months," Mourinho said.
"After these three months you have an idea who can reach domestic finals, who can fight for the title, who's out of the running for the title.
"It's a lot about November, December, January. It's a moment where the squad is not big enough. It's a moment where everybody feels part of it and every player must have an answer when the team needs him. It's a moment I enjoy."