The 40-year-old met with Inter president Erick Thohir on Sunday to discuss his future at the club once his contract expires this summer.
"I am very happy, because I think that I will continue to be a part of Inter," Zanetti said to www.inter.it. "I never had any doubts about that, as there has always been absolute clarity with the president.
"The most important thing is that this marriage will continue."
Zanetti joined Inter in 1995 and is expected to hang up his boots at the end of this season.
Thohir is ready to reward the former Argentina international with a new role at the club.
"Zanetti is a great player," Thohir said. "I want him to focus on the season, and he agrees.
"There are only three months left, then after this season he can join the family."