Icardi helped Inter qualify for the Champions League but the skipper – who reportedly has a €110 million (£97m/$129m) release clause – has been linked with Juventus, Real Madrid, Chelsea, Bayern Munich and Manchester United.
Zanetti was asked about Icardi's future but the former Inter captain said he is not concerned over the 25-year-old forward.
"It's disappointing he's not going to the World Cup, as he has proved he fits in with the Argentina squad," Zanetti told reporters.
"When you have a champion like him in the team, it's only normal to receive many offers, but Mauro is the captain and a reference point for Inter.
"We are happy to have him here and he is happy to be with us. We are not worried by transfer speculation, because he manifested his desire to remain and we in the Champions League, so wish to continue together.
"Every time he steps on to the field, he shows how much he cares about Inter."
Icardi scored a joint-high 29 goals in 34 Serie A games in 2017-18 as Inter finished fourth in the standings.