Leonardo Jardim's side are reportedly seeking a successor to Radamel Falcao, who has been linked with Turkish club Galatasaray.
Free agent Daniel Sturridge, who left Liverpool at the end of his contract in June, is also reportedly a target for the French club.
Icardi, however, will not be moving to the French Riveria before the transfer window closes on September 2.
"He will not go to Monaco," Nara said simply to TyC Sports.
Even with a move to Monaco being ruled out, Icardi is still likely to be on the move before the transfer deadline.
His relationship with the club broke down last February when he was dropped by then coach Luciano Spalletti and stripped of his captaincy amid reports of contractual disputes between himself, the club and Wanda Nara.
He returned to action before the end of the season, but Inter have made it clear that he no longer features in their plans under new boss Antonio Conte.
The 26-year-old didn’t travel with the rest of the Inter squad for their pre-season tour of Asia last month, instead returning to the club’s training base on his own.
Icardi even had his number 9 shirt taken off him, with new €80 million (£74m/$90m) signing Romelu Lukaku designated that squad number ahead of the new campaign.
However, that move currently looks unlikely with Juve boss Maurizio Sarri claiming he already has too many players in his squad, with as many as six needing to be sold before the transfer deadline.
Those thoughts were echoed by Juve defender Giorgio Chiellini, who claimed a move for Icardi would be “fantasy football” given the number of attacking options already at the club’s disposal this season.