The 40-year-old veteran ruptured his Achilles tendon last April and has made only seven appearances for Walter Mazzarri's side this campaign.
Zanetti, whose contract at San Siro expires in June, played down links to Stamford Bridge in February, but has admitted during the international break that he has yet to make a final decision on whether to pass on the Nerazzurri captaincy.
"Inter have given me so much and I am very proud," Zanetti said at a special presentation to receive the 'Cartellino Viola' Fair Play award. "This season I wanted to return from a serious injury, show I can be useful and keep playing.
"The most important thing is the future of this team, qualifying for Europe and finishing the season well. Then we will see - I am here and available.
"The bond between Inter and I will last forever. At the end of this season, thanks to the great relationship I have with president Erick Thohir, we will assess what is best for Inter."