Inter are holding out for offers of more than EUR60million for Mauro Icardi, according to club president Erick Thohir.
The club captain has been tipped to make a move to Napoli to replace new Juventus signing Gonzalo Higuain, with his wife and agent, Wanda Nara, claiming that Inter had failed to offer him a sufficiently improved contract.
Thohir said this week that Inter had already rejected a bid from Maurizio Sarri's side for the striker, insisting that they had no desire to sell him to a Serie A rival.
But the Indonesian businessman, who remains in his role at San Siro despite having sold a majority stake in the club to Suning Holdings Group, has suggested that an offer of over EUR60m could be enough to tempt them in to selling.
"All of us are hoping that number goes over EUR60m," he told the media in New York when asked about a reported new bid from Napoli. "But for us, that isn't important at the moment.
"Inter will be here for hundreds of years yet. Inter is made of individuals who can change. This happens every year."
Thohir did stress again that Icardi was a vital part of the side, however, adding: "He's a very important player for the team, he's our captain. We're building a team and we have to look at the dynamic."
The future of head coach Roberto Mancini has also been called into question, with reports suggesting he has grown frustrated over a lack of transfer activity so far in pre-season.
Thohir has admitted that he does not always see eye-to-eye with Mancini but insists their working relationship remains strong.
"The relationship with Mancini is good, although we've had some disagreements," he said.
"There are some differences in views, but the important thing is to work for the team."