The coach has reiterated his faith in his captain, Walter Samuel and Diego Milito, insisting they remained important to the club's attempt to achieve an European berth
Goal understands Chelsea boss Jose Mourinho has made an informal move to bring Zanetti to Stamford Bridge in a player and coach role.
But Mazzarri deflected suggestions the 40-year-old's future is elsewhere, stating the defender remains as integral to the squad as ever after his comeback from tendon surgery this season.
"There's no problem with Zanetti. I have a fantastic relationship with him," the trainer told reporters. "I see him in training every day.
"He's important to us both when he's playing and when he's not. He helps me out with the younger players, with everyone, then I pick the team.
"If he's not playing at the moment it's because I want to keep faith with the players who are performing well in the positions he plays in."
Fellow treble veterans Diego Milito and Walter Samuel have been linked with a Nerazzurri exit come season's end, but Mazzarri reiterated his faith in them in the matches to come.
"Samuel gives us so much beyond his technical ability because he's the sort of character I'd like to see in every area of the field," he continued.
"He always brings us something extra, bite and confidence. He's a reassuring presence for the rest of the team.
"Milito is running well, perhaps even more than he was before but he still needs to find that edge he had before he got injured. In any case he's getting there."
None of the Argentine contingent are expected to start against Cagliari however, as the San Siro outfit aim to consolidate a place in Europe for next season.