The 25-year-old said that he would be thrilled to come back to the Stadio Olimpico, but conceded that the decision lies in the hands of Biancocelesti president Claudio Lotito
The Argentine attacker played an important role for the Nerazzurri under Andrea Stramaccioni in the last few months of the campaign after being relegated to a bench role during Gian Piero Gasperini and Claudio Ranieri's ill-fated stints.
Inter are reportedly willing to exercise their buying option for Zarate, but the 25-year-old has given a strong indication that he will ply his trade at Lazio next season.
"My situation is clear: I am owned by Lazio," Zarate told Il Corriere dello Sport. "If there is a club who want me, we will talk about it.
"If president Claudio Lotito wants to keep me, then that is fine. I will return to Lazio and give my best.
"I left Lazio because I did not get on with Edy Reja. If Lotito wants me, I would be very happy. We will see what happens."
Zarate went on to share his disappointment with Inter's season, as the San Siro outfit finished a disappointing sixth in Serie A.
"Everything went wrong," he added. "It was not a good season, not just for me.
"Aside from Diego Milito, who scored many goals, almost no one played at their true level.
"With three different coaches, it was a strange campaign, but that is over now. What I want is to play again and have fun."