The Spaniard was again the preferred choice as Chelsea drew with West Bromwich Albion on Saturday, and Mourinho insists that Cole will need to put up a fight to get back in the team.
"I can make mistakes, I can be unfair, but I always give a lot of thought to my decisions," he told reporters. "I decided for Azpilicueta to play against Schalke [in the 3-0 Champions League win] and he was fantastic. 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 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 to work and fight and the position is there waiting for him, no problem."
Cole was dropped following Chelsea's 2-0 defeat to Newcastle United earlier this month.