The former Nerazzurri star, who is now vice-president of the Serie A club, believes his fellow Argentine will agree to stay on at San Siro
Transfer talk is building around the talented 22-year-old as he continues to thrive on a European stage.
The 2018-19 campaign was an adjustment one for Lautaro, as he settled into new surroundings at San Siro on the back of a high-profile switch from Racing Club.
He has burst into life in 2019-20, with 16 goals recorded through 31 appearances for Inter.
It is reported that he has a €111 million (£93m/$120m) release clause in his contract, with Liga giants Barca among those said to be prepared to pay that price for such a hot prospect.
Those at Inter are aware of the speculation, but they remain confident that a prized asset can be persuaded to stay put.
Zanetti, who is now vice-president of the Serie A heavyweights, told Radio Continental of a fellow countryman: “We are happy with Lautaro and Lautaro is happy with Inter.
“What he is doing here with us is fantastic.
“He also demonstrates that with the national side in Argentina. I see him continuing in Italian football.
“He is the joy of the last generation of Argentine footballers. He is only 22 years old and has a great future ahead of him.”
Zanetti’s comments echo those which have come out of Milan on a regular basis over recent weeks.
Inter boss Antonio Conte believes Lautaro is fully committed to the title-chasing squad that he has pieced together, saying: “The boy is fully concentrated.
“He is doing well and must continue in this way.
“He has grown a lot over the last year and is only 22. He is committed and I am happy to have him available.”
Inter CEO Beppe Marotta has also sought to bring the unwelcome exit rumours to a close by pointing out that Lautaro would have to request a move in order for any offers to be considered.
He told Sky Sport Italia: “Rumours regarding Lautaro? He is very young and improving. He is only interested in wearing the glorious shirt of Inter.
“This club has nothing to envy others of. Players can leave only if they ask to leave.”