Celtic have entered the race with Leeds United and Cardiff City for Anthony Stokes.
The Clarets have joined Leeds United and Cardiff City in pursuit of the 26-year-old frontman and they could make an offer before the close of the January transfer window.
Stokes has scored eight goals this season and Sean Dyche reportedly believes that he could be a player to enhance his options.
Burnley are fighting against the drop in the Premier League, but are currently above the drop zone and Stokes would be expected to fire them even further up the table if he did arrive at Turf Moor.
What's the impact for Burnley?
The transfer would be an intriguing one as Stokes has not been particularly prolific in the Scottish Premiership and his previous showings in England haven't suggested that he could cut it at the top level.
Although Stokes has had to play out on the wing for the majority of the campaign with the Bhoys, his ratio of one goal in more than every three games would be a concern.
Burnley also, arguably, don't need any more striking options. Dyche already has a packed forward rank and there are other areas of his squad which require a more urgent upgrade.
If Stokes did sign for Burnley, he would join Danny Ings, Ashley Barnes, Sam Vokes, Marvin Sordell and Lukas Jutkiewicz at the Lancashire club and his place in the starting line-up would be far from guaranteed.
It would, therefore, be a surprise to see Dyche invest some of his limited transfer funds in another striker, considering Burnley's budget is the smallest in the Premier League.
Burnley have an obvious need for a central-midfielder before the window closes and by buying Stokes Dyche could be spending precious money on a player who isn't desperately needed by the club.