Mourinho told reporters that the Cameroonian had a "grade one muscular injury" to his hamstring.
Sunday's Premier League match with Southampton is the first of nine matches in December for the Blues, who return to Stamford Bridge bidding to show improvement from their last home match, the 2-2 draw with West Brom, and most recent result, Tuesday's loss at Basle.
"Now is time for the squad," Mourinho said.
"And now is time for everybody to feel that they have a chance, when we play now Sunday, Wednesday, Saturday, Southampton, Sunderland and Stoke.
"The SSS week, everybody will have a chance."
Cole's absence in recent weeks - with Spain right-back Cesar Azpilicueta preferred - has been a surprise despite the England left-back's niggling rib problem.
"Ash will play for sure and will have the chance to show that he's fine," Mourinho added.
The Portuguese dismissed reports of a bid for Real Madrid left-back Fabio Coentrao.
"I don't want Portuguese players," Mourinho said. "I always had them, but I think in this moment it's enough. Only Hilario is the remaining one and we don't need (others)."
A move for Colombia striker Jackson Martinez, currently at Porto, was also downplayed, with Mourinho happy with his forward options Fernando Torres, Samuel Eto'o and Demba Ba.
Mourinho added: "It's not true what I read a couple of days ago, that the agent was in London and was meeting with me or Chelsea directors. It's not true at all.
"In the January market we are not going to buy any striker. We will go to the end of the season with Fernando, with Samuel and with Demba. Nobody to go in, nobody to go out."
Asked again about Lukaku, Mourinho called on the Belgium striker to reveal why the loan move took place.
"Romelu likes to speak," Mourinho said.
"He's a young boy. But the only thing that he didn't say is why he went to Everton on loan.
"My last contact with him was to tell him exactly that. 'Why you never say why you are not here?'
"It's something that he should say, because he likes to speak, the reason why he is not with Chelsea and he is in Everton."
Torres is available again after returning in the Basle loss in place of Eto'o, who went off injured and faces around two weeks out with a groin injury.
David Luiz missed the trip to Switzerland and could again be absent with his knee injury despite returning to training.
Chelsea have won 38 of the last 42 Premier League points on offer at home, but needed a controversial penalty against West Brom on November 9 for Mourinho to extend his unbeaten league record at Stamford Bridge to 66 games.
Following last Saturday's comprehensive defeat of West Ham, the Basle trip, which saw Chelsea advance to the Champions League knockout stages despite a second defeat to the Swiss side in Group E, highlighted the team's inconsistent performances.
Mourinho afterwards attributed the limp display, where his side failed to muster a meaningful shot, to tiredness, but he may not be as forgiving in future.
"I never tolerate, but I have to live with it," he said.
"I didn't like the performance, of course not, and we will try everything to not repeat (it)."
The pressure on Sunday is on Chelsea to show that Tuesday's result was a blip.
Mourinho added: "If I forget the performance from the last match, our situation is fine.
"We are in a close distance to the (Premier League) leader, we are qualified for the last 16 in the Champions, we will play in the Capital One Cup quarter-final. We are okay. Our situation is okay.
"We have to improve stability in our game, we have to improve aspects, also individually we have to improve, especially the young players, but we are okay."
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