Burnley's co-chairman John Banaszkiewicz has described recent offers that the club have received for Charlie Austin as "cheeky".
Earlier this month it appeared that the striker was bound for Premier League side Hull City, but the move fell through due to concerns over his medical test.
Interest in the 24-year-old is still high though, Banaszkiewicz has revealed that bids over the last few days have not been given any consideration.
"There has been some interest in him, but we would prefer to keep him if we can," Banaszkiewicz told the Lancashire Evening Telegraph. "We have had a few cheeky bids, but they've not been worth discussing. Some clubs have come in looking for a bit of a bargain.
"There's nothing really to say there. It is still early days and he is still wearing a Burnley shirt. I'm hoping that he will stay and we're doing our best to try to keep him."
Austin scored 28 goals in all competitions last season.