Having netted 16 goals in Serie A and the Champions League this season, Martinez has been frequently linked with a summer switch to Barcelona.
However, despite the Argentina international possessing a release clause in his contract, Zanetti feels that his compatriot could choose to remain with his current club.
Zanetti told Sky Sport Italia: "I'm happy to talk about Lautaro because when we signed him we had been following him for some time. He was one of the most promising players in Argentine football and [Diego] Milito thought he'd have a big future.
"Now he's an asset for us and he's grown a lot. I see him training every week. He's happy with us and I hope he stays for a long time."
Martinez has a contract at Inter until the end of the 2022-23 campaign. body check tags ::