Burnley are thought to have turned down an offer in the region of £2m for captain Jason Shackell.
Derby made the bid over the weekend, but the Clarets are standing firm.
Neither club has commented officially, but Derby will have to up their interest if they are to persuade Burnley to part with the former Rams skipper.
Derby are believed to be pondering a fresh offer.
Shackell was signed by Eddie Howe from Derby for £1m three summers ago and has been a virtual ever present since.
He has one year remaining on his contract.