The 40-year-old has been with the Italian side since 1995 but had been linked with a move to Stamford Bridge, with the pair having worked together at San Siro.
It was reported that Mourinho was interested in offering Zanetti a role as player-coach but the former Argentina international insists he is committed to Inter.
Despite making just four starts in all competitions this season, after recovering from an Achilles injury, Zanetti also said he is happy with his role under Walter Mazzarri.
"Honestly, I have a great relationship with Mourinho, we often talk, but we never talked about these things," he told Inter Channel.
"I believe that Inter fans know what I feel about this shirt. I always said, to me, Inter is my life and that... my desire is to stay here. Say no more.
"Since I'm a player I think there are two possibilities: either play from the start or be on the bench and then be able to enter.
"I will be able to make my contribution, but I think that everything is going in the right direction."
