The Argentine centre-back has been linked in the Italian press with a move to Stamford Bridge in a swap offer that would see Carvalho head in the opposite direction to the San Siro.
But the 28-year-old, who made 21 league appearances for Inter last season, insists there has been no contact with anyone at Stamford Bridge and that he is happy at Inter.
Burdisso told calciomercato.com: "I have spoken to Jose Mourinho, who told me that he is happy with me and that I have a lot to give to Inter.
"My relationship with Mourinho is excellent and I hope that it remains like that in the future.
"Last season was a positive year for me and my wish is to remain at Inter."