The Hammers have seen two offers - the latest worth £27million - rejected over the last week and are understood to be preparing a third.
“Do players have a price at any club? Yes, they do," Dyche said. “At a club like this, eventually there is a price.
"We've seen across football that eventually a day comes when someone hits a certain number, all clubs have to make a decision.
"If that comes, the chairman and the board will control that situation, but we are in a very strong position and are not in the business of letting our best players go on the cheap.
“Not many clubs around the world will refuse everything they are offered, eventually they make a decision. That is not there yet and nor do I want it."
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