The Chile international has been strongly linked with a move away from Udinese this summer, with Barcelona, Inter Milan and City in the race to acquire the 22-year-old winger.
"Sanchez? The right offer has yet to arrive," said Pozzo. "Thirty five million euros is not enough for Sanchez. We already turned down a similar offer. A higher offer is needed."
He added: "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 is under contract with Udinese until June 2014 and scored 12 goals this term to help the Bianconeri qualify for the Champions League next season.