The 40-year-old midfielder's current deal with Inter ends next summer and Zanetti has expressed his wish to remain with the Nerazzurri for a further year.
"I would like to remain and give my contribution to this great family that Inter is," Zanetti told www.inter.it.
The Argentinian star returned to play in Sunday's 2-0 win over Livorno for the first time since rupturing his Achilles tendon against Palermo back in April.
"The game against Livorno was a game full of emotion," he said. "After so much time away from the pitch, I dreamt of such a night."
Zanetti, who joined Inter from Argentinian outfit Banfield in 1995, is 43 appearances shy of breaking the Serie A appearance record currently held by AC Milan legend Paolo Maldini, who made 647 league appearances.
"With Inter, the aim is to return to have a starring role and for the time being we are doing this," Zanetti said.
"The Italian league is difficult and there are many teams that compete for the same aims as we do.
"But we are working well and we want to fight for something important."
Sunday's win lifted Inter to fourth in Serie A, three points adrift of Napoli, who are third and hold the last Champions League qualifying spot.