Director Rinaldo Sagramola has admitted there has been interest from the Nerazzurri but is hoping the young striker will sign a new deal at Stadio Luigi Ferraris
Reports in Italy suggested a transfer had been finalised to bring the attacker to San Siro, but these seem to be wide of the mark.
The 19-year-old has scored eight Serie A goals in his first season in Italian football, including both strikes in a 2-1 win over leaders Juventus.
And Sagramola admitted there has been interest in Icardi from Andrea Stramaccioni's side, though the club are hoping the player will sign a new contract.
"I deny the reports. These voices of an Inter sale are not true. Inter have told us they are interested, but there is some way to go before saying that we’ve sold him," he told Gazzetta Giallorossa.
"It would also be against federation rules seeing that the player is still under contract with us.
"We’re actually waiting for the boy to respond to our offer to extend his contract."
Roma have also been linked with the teenager, but Sagramola denied any knowledge of the Stadio Olimpico outfit looking to sign the forward.