The Premier League side were hoping for a clean run at their former player.
However, the 29-year-old was so impressive last season that other clubs are alerted to his £5million with £5million release clause.
There are up to six teams vying for his signature, per the Lancashire Telegraph.
Burnley hope that a return to his old side and a move back to the Premier League will be enough to tempt Rodriguez in their direction.
The veteran bagged 22 goals in the Championship last season.