"I have a great rapport with Mourinho. We hear from each other frequently, but we've never discussed these things," the 40-year-old Argentine told the Inter Channel.
"I believe the Inter fans know how I feel about this shirt. I've always stressed that this club is my life and my home. And it's my desire to stay here. I don't need to add anything else."
Zanetti's contract with Inter runs out at the end of the season and media reports in England suggested that former Inter manager Mourinho wanted Zanetti in a player-coach role.
Zanetti has been at Inter for nearly two decades, helping them win five Serie A titles.
He played under Mourinho during the Portuguese's two-year spell at the club, when they won the Champions League and two league titles.
Inter are fifth in Serie A under coach Walter Mazzarri and host struggling Cagliari on Sunday looking to close the 11-point gap separating them from third-placed Napoli who host Genoa on Monday.