Cole watched the last two Chelsea games – a 3-0 win over Schalke in the UEFA Champions League last week and the 2-2 draw with West Brom on Saturday - from the bench as an unused substitute after Mourinho opted to give Azpilicueta the nod.
Mourinho feels his decision to play Azpilicueta - a right-back by trade - ahead of Cole has paid off, but told the England international that he will be welcomed back into the starting XI if he shows more "fight".
"I decided for Azpilicueta to play against Schalke and he was fantastic," said the Chelsea manager. "On Saturday, he was very good again.
"Ashley is a top professional, he is a fighter.
"He has to work hard, to fight hard because the place (in the side) is his place.
"Of course, it is not Azpilicueta's best position, and it is not a position where Ashley can think that he is in trouble now.
"No, he has to just work, fight and the position is there waiting for him, no problem."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.