Throughout the 2019/20 season, the Argentine has been rumoured to be a key target of the Blaugrana, with the club keen to see him hook up in a new-look attacking line-up alongside compatriot Lionel Messi.
However, since Ronald Koeman's arrival as a replacement for Quique Setien any reports of a swoop for Martinez have quietened, with the Dutchman focusing on other targets like Gini Wijnaldum and Memphis Depay.
Messi reportedly wants Martinez at Barca, and any move for his national team colleague could in some part mend the fractured relationship between the club captain and the club hierarchy.
However, according to Zanetti, there have been no discussions this summer.
"In his case, being just a young player with such potential, it's normal for other teams to look at him," the Inter legend told Libero on TyC Sports.
"But what I see each day is a Lautaro who wants to stay in Italy.
"He knows that he's at a great club and that he's improving a lot thanks to the coach [Antonio Conte]."