Carrick made his second Premier League start of the season in a 1-1 draw with Arsenal on Saturday and Mourinho was impressed by the veteran midfielder's performance.
With Carrick's existing contract set to expire at the end of the current campaign, Mourinho indicated he will be looking to keep the former England international.
"Michael is 35 years old," Mourinho said. "With such an intense game he was having some cramps in the last period, which is normal.
"It is very sad to know that time flies for every one of us. He is such a fantastic player and it is a pity, I always loved him, but instead of being his manager when he was 25 I am his manager when he is 35.
"We have a good understanding. We know when he can play. We know when he is ready and when he needs a rest.
"I am still having Michael Carrick and probably for one more season. That's life."
"He is adapting much better in relation to the intensity of the competition and he is much more confident," Mourinho said.
"Obviously he plays with some guidelines over his position but at the same time with some freedom to occupy some attacking areas where he feels and thinks he can be important.
"He is comfortable on the pitch. That is the best way of saying it."