Tomkins, 22, has been linked with a £3million move to the West London club following his superb displays for the Hammers this season.
QPR boss Neil Warnock is ready to bring in a number of new players in January and wants to bolster his defence.
Tomkins has played a major role in helping West Ham cement their position in the top two of the Championship.
But West Ham co-owner David Gold said: "He's not for sale for £3m. Nobody is up for sale.
"There's no plan to sell. We'll do all we can to keep our top players. Our goal is promotion."