Martinez won the World Cup with Argentina in December and has been touted as one of Mauricio Pochettino’s first targets at Stamford Bridge.
The former Tottenham manager is expected to be appointed as the third head coach of the Boehly-Clearlake era after verbally agreeing a three-year contract in west London.
Chelsea have struggled for goals all season despite a major recruitment drive over the last two transfer windows, with Kai Havertz the club’s top scorer with seven.
Martinez, meanwhile, has scored 25 times in 52 appearances across all competitions.
“I’m very happy for Lautaro, who grows with us every year,” said Zanetti.
“He’s a reference for the team. He is so important for us.”
Romelu Lukaku is eager to stay at San Siro and Chelsea officials will talk to their Italian counterparts about the Belgian’s future.
Inter goalkeeper Andre Onana is under consideration at Stamford Bridge too as Pochettino targets a new option between the posts.