The "numbers would need to be considerable" for James Tarkowski to leave Burnley during the transfer window, says manager Sean Dyche.
The defender, 27, has been the subject of three bids from West Ham, with the most recent thought to be around £30m.
Burnley are yet to start their Premier League campaign and have not made any signings since finishing 10th last season.
"We want to keep our best players," said Dyche.
"I don't see why any player would leave here at this moment in time and if they did I think the numbers would need to be considerable for it to be considered."
Goalkeeper Joe Hart has left Burnley to join Tottenham, winger Aaron Lennon moved to Turkish side Kayserispor, midfielder Jeff Hendrick was signed by Newcastle and defender Ben Gibson has left for Norwich on loan.
Dyche says "the main difficulty is finance" when it comes to bolstering his side, who face Sheffield United in the Carabao Cup on Thursday (17:30 BST) and Leicester in their Premier League opener on Sunday (19:00).
He added: "The group needs reinforcements, we lost players at the end of lockdown. We are looking but it is not an easy situation and the finance is what it is."