With the January transfer window opening, a number of Hammers players including Craig Bellamy, Matthew Upson and Scott Parker have been linked with moves away from Upton Park.
West Ham were hit by two major financial setbacks in 2008 with Icelandic owner Bjorgolfur Gudmundsson suffering huge financial losses in the recession while the club still face the prospect of paying millions of pounds in compensation to Sheffield United as a result of the Carlos Tevez affair.
Duxbury told the club's website that all offers for players would be considered but added that manager Gianfranco Zola would make the final decision on who came or went.
"We have no intention of selling our best players, nor are we telling the manager to do so," Duxbury said in a statement on the website.
"It may be that some players are allowed to leave but no one will be going unless the manager thinks it is in the best interests of his team and it is right for the club."
However, he also said: "As a club we will look at every single approach rationally.
"We must not be afraid of interest in or bids for our leading players. Each approach will be considered in terms of fee, fitness, form and where the manager thinks the player is in his career."
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