Brayford has entered the final year of his existing deal with the Rams and the club are keen to extend his stay at Pride Park.
The right-back was the subject of a bid from Wigan last month with Derby rejecting the offer because it fell short of their valuation of the player.
Brayford, 25, had previously attracted interest from Premier League newcomers Cardiff as well as West Ham.
Following the Rams' 2-0 win at Bristol Rovers on Friday night, manager Nigel Clough told the Derby Telegraph: "We are going to sit down with John next week and have a chat.
"The situation hasn't changed much. I don't think John really wants to go. I know the window is open for another four weeks after the start of the season but it would be nice to try and get something sorted before then, if possible."
Brayford has made 118 appearances, all but one of them starts, since joining Derby from Crewe in the summer of 2010.