The Clarets splashed the cash to bring in James Trafford from Manchester City in the summer and he has slotted in as their number 1 goalkeeper.
Muric, who was between the sticks as Burnley secured promotion to the Premier League, has seen himself pushed out of the picture.
The shot-stopper, according to Sky Deutschland, remains fully focused on Burnley, but he wants to play on a regular basis and he is not short of admirers.
Several sides are keen, including Spanish giants Seville and German outfit Union Berlin.
It is suggested that Muric could possibly move away from Burnley in the January transfer window on loan with an option to buy.
Muric put pen to paper to a four-year deal when he landed at Turf Moor in the summer of 2022.
The shot-stopper will continue to push to try to dislodge Trafford between the sticks, but may have a decision to make in January.
