Everton are on the hunt for a new man in the dugout after dismissing Rafael Benitez earlier this week.
Mourinho has been earmarked as one of the bookmakers’ favourites to take charge at Goodison Park.
The Portuguese is still in his first year in the Italian capital, having signed a three-year contract last summer and he insists he is happy to remain in his current surroundings.
“In terms of emotion, passion, empathy, of being happy working with Roma, I say I am 11 out of 10," Mourinho told Sport Mediaset after Roma beat Lecce 3-1 in the Coppa Italia on Thursday.
"I am truly, very, very happy to be at a club where I feel the people trust me. I couldn’t be happier than this.
“In football terms, playing to finish between fourth and eighth place is obviously not what I want, but this is a moment of a different project for me and we will be better off next season.
“I won’t deny in the first half I did feel frustrated, as our performance was horrible. Having said that, I am happy right now and would not change this Roma project for any other.
“I gave my word for these three years and I will not leave before the three years are up. This is my project too."
Roma have been drawn against Italian champions Inter in the Coppa Italia last-eight.
"There’s a long way to go, we have a few more games and for me there’s no doubt Inter are the strongest team and overall squad of the league and the Coppa Italia," Mourinho said.
"We therefore got the worst possible draw, but we will go there and try to cause a surprise. We’ll see if it’s possible."
