The 24-year-old joined the Clarets from Premier League champions Manchester City in the summer of 2022, and quickly cemented himself as a regular for Vincent Kompany's side in the Championship.
Burnley cantered to the second-tier title with Muric playing an important part as first-choice keeper, keeping 17 clean sheets in 41 league appearances as the Turf Moor club finished ahead of second-placed Sheffield United.
The Kosovo international moved from the Etihad Stadium to Lancashire just over a year ago and has since featured 43 times for the Clarets following various loan spells in the past at Girona, Willem II and Adana Demirspor.
According to Sky Deutschland, Union Berlin are monitoring Muric's situation with Burnley, and the Bundesliga side could be set to make a move for the keeper in the near future.
The report claims that the German outfit are considering an approach for the 24-year-old in the January transfer window - a deal which could see the shot stopper turning out in the Champions League knockout stages in 2024.
It is understood that Urs Fischer's men would be looking to secure Muric on a loan spell with an option to buy at the end of the 2023-24 campaign, although there is no mention of an obligation to buy in the agreement.
After finishing fourth in the Bundesliga last term and booking their spot in the Champions League for the first time, Union recruited some notable names during the summer window, including Leonardo Bonucci and Robin Gosens from Juventus and Inter Milan respectively.
A New Year switch to Germany could potentially enable Muric to play in UEFA's elite club competition for the first time in his career, however there are no guarantees that the Berlin club progress into the knockout stages.
Following defeats to Portuguese side Braga and 13-time winners Real Madrid in their opening two matches, Union sit bottom of Group C, three points behind second-placed Napoli, who are fresh from their first Serie A title this century last term.
The summer arrival of James Trafford to Burnley has seen Muric lose his place as first-choice keeper at Turf Moor - which is largely unsurprising considering that the Clarets paid £19m for the England Under-21 international.
Muric has failed to feature in any of his side's Premier League matches to date this campaign, however Kompany has handed Muric a pair of starts in the EFL Cup successes at Nottingham Forest and League Two outfit Salford City, with the top-flight newcomers keeping a clean sheet in both matches.
Muric is still the number-one option for his national side, playing the full 90 minutes as Kosovo put three goals past minnows Andorra in a European Championship qualifier last Thursday.
It is largely expected that Trafford will keep his place in between the sticks for the Clarets as they return to action after the international break with a trip to Thomas Frank's Brentford on Saturday.