Burnley tried tempting last year's play-off semi-finalists with a £3m offer, but the Clarets' offer fell way below Derby's valuation of the player.
Newly promoted Burnley have now made a new offer for Hendrick and are supposedly offering James Tarkowski and Tendayi Darikwa to move on loan as part of the deal.
Hendrick enjoyed a successful Euro 2016 with the Republic of Ireland and may be on a number of Premier League club's radars.