Markovic joined from Benfica in a £20 million deal in 2014, but has made just 34 appearances for the club, spending the majority of his time on the Reds’ books away on loan.
The Serbian joined Fenerbahce on a temporary deal in 2015, before splitting last season between Sporting CP and Hull City, enjoying a productive five months with the latter.
He was expected to secure a move away from Merseyside last summer, but ultimately remained as part of Jurgen Klopp‘s first-team squad.
Spartak, one of the Reds’ opponents in the Champions League group stage, are among the interested parties, and “have expressed an interest” in a deal.
They could face competition from West Brom, however, with Alan Pardew “understood to be considering an approach” as he looks to bolster his attacking options at the Hawthorns.
Still only 23, Markovic has 18 months left on his contract with the Reds, but has struggled to impress during his time at Anfield.
In his 34 appearances for Liverpool he has scored just three goals, assisting one other, with standout performances few and far between.
It can be argued that he was not afforded enough opportunities by either Klopp or Brendan Rodgers, with his stint under the latter largely seeing him deployed at wing-back.
But his marginal role suggests a failure to adjust to the demands of life at a top-level Premier League side, and a January move would benefit all parties.
Last summer it was claimed that Liverpool were looking for a £16 million fee for the winger, but their asking price is likely to be significantly lower at this stage.
Markovic is unlikely to be the only player to leave the Reds between now and January 31, with Daniel Sturridge among those also heading towards the exit.