Argentina international Icardi has been linked with a switch to the Ligue 1 side after being told he can leave San Siro.
The Inter captaincy was taken off the player last term and he appears to have no future at the club under coach Antonio Conte.
Nara, however, has ruled out a Monaco move before the French and Italian transfer windows close on September 2.
"He will not go to Monaco," Nara said simply to TyC Sports.
Monaco are reportedly seeking a successor to Radamel Falcao, who has been linked with Galatasaray.
Free agent Daniel Sturridge, who left Liverpool at the end of his contract, is reportedly a target for Leonardo Jardim's side.