Icardi has regularly been linked to the Spanish giants, who have won the Champions League in each of the past three seasons.
But the striker, having hit six Serie A goals so far this season, indicated last month he could sign a new Inter deal.
Zanetti is not worried about the prospect of managerless Madrid making a move for Icardi in the January transfer window.
"Icardi is our captain and our reference, but he is also very happy at Inter," Zanetti told Marca. "We are not aware of any interest from Madrid.
"We are aware that Inter is a healthy club so that we do not have to sell and continue to respect [Financial] Fair Play."
Madrid have put Santiago Solari in temporary charge following the sacking of Julen Lopetegui, whose ill-fated tenure lasted 14 matches.
"I know Santi very well and I know what Real Madrid means to him," Zanetti said. "He has wonderful values as a person, he is a very intelligent guy, a very respectful guy with a great sense of belonging.
"He is developing and this step is going to be relevant for him. Knowing the atmosphere of Madrid so well is the best solution to get out of this situation. He is very prepared for it.
"You have to be patient with the coaches and give them the necessary time. It is important that the club is convinced of this, that a strategic plan is made and not to doubt when the bad moments come."
But Zanetti feels Conte, a three-time Serie A winner during his time at Juve, could be a good option for the LaLiga side having left Chelsea at the end of last term.
"Due to his style, great personality and experience, it would not surprise me if Madrid look at him," Zanetti added.