The Chelsea boss insists the left back has caused him no problems despite falling behind Cesar Azpilicueta in the pecking order at left back in recent matches.
The England international defender has regularly found himself on the bench in recent weeks, with Cesar Azpilicueta preferred at left back.
But despite dropping him, Mourinho has praised Cole's attitude in training as he bids to reclaim his place in the Chelsea starting XI.
"His attitude is phenomenal, as always," he said. "He has the same attitude today that he had when he trained with me for the first time. Even through the difficult period, yes. Ashley's attitude is an example.
"Azpilicueta is playing fantastic."
Mourinho is hoping his charges can bounce back from a midweek 1-0 Champions League defeat in Basel with victory over high-flying Southampton on Sunday.
"I never tolerate a loss," he said. "But I have to live with it. We will try everything not to repeat it. We analyzed their individual match performances and today's [Friday] training session was very good.
"Now is the time for the squad. It's time for everybody to feel that they have a chance."
But the former Real Madrid coach is aware of the challenge posed by Mauricio Pochettino's side, who would leapfrog Chelsea in the table with a victory.
"Southampton are very compact and solid," he added. "They are doing well. They will have a very good season."