The Slovakia international is reportedly one of two Serie A defenders Mourinho wants to bring in to the club in January, with Milans Alessio Romagnoli also on the Portuguese managers shortlist.
According to newspaper reports Inter had valued Skriniar as high as £76million but are now accepting he could be let go for a fee in the region of £50m, despite having signed a new contract in the summer.
The 23-year-old says he is glad to hear of the interest but has poured cold water on the suggestion he will leave the San Siro this season.
When some coach like Jose says that he is looking for a player like me or somebody else, its always nice, but I dont know why these rumours continue, he told ESPN FC.
Ive not said anything to anybody, just what you can see on the web.
Even if Jose is one of the most famous, best, greatest coaches in the world, its not something I think of because Im playing for Inter and am happy here at Inter.
Im happy in Milan, its a great city, even when my parents or friends come here, we have a look around and Im happy here and relaxed here. When the results are going well too, its all even better.”