The Argentina international is a favourite of Barca captain Leo Messi, who has recommended his signing to the club's board.
Barca know they can land Martinez for a set fee of €111m - thanks to his buyout clause.
But Zanetti insists, "If Barça can sign Lautaro Martinez? The idea is that he stays with us. He is only 22 years old and I hope he stays here for a while.
"At Inter he can already be an important player."