Udinese owner Gianpaolo Pozzo says potential suitors must part with more than 35million euros (nearly £31million) to land Alexis Sanchez.
Manchester City, Barcelona and Inter Milan are thought to be in the race to acquire the 22-year-old winger.
Pozzo says the Serie A outfit have already turned down a similar offer for the Chile international and potential suitors must slash out more.
He told a press conference: "Sanchez? The right offer has yet to arrive.
"Thirty five million euros is not enough for Sanchez.
"We already turned down a similar offer. A higher offer is needed.
"Sanchez is a very important player and we will see what happens but I have already spoken to Alexis and his agent.
"Alexis is a player that has a plenty of requests but his value is high.
"It's not an easy transfer for those that want to buy him.
"He (Sanchez) and his agent are intelligent people and they are the first to understand that we cannot give him away on the cheap.
"Moreover, if clubs do not consider his value, it is better that he remains in Udine."
The South American, who is under contract with Udinese until June 2014, scored 12 goals this term to help the club qualify for the UEFA Champions League next season.