Markovic, who is spending the season with Sporting CP, left the field midway through the Portuguese side’s 1-0 Champions League defeat to Legia Warsaw last week.
He was then missing for the Derby de Lisboa on December 11, which it now transpires was due to injury.
According to A Bola, Markovic has picked up an abductor problem that will keep him out for action for an indeterminate period.
Sporting’s medical department are said to be unwilling to allow Markovic to return until his problem is 100 percent clear, and therefore no return date can be set.
This marks yet another setback for the 22-year-old in his burgeoning career, with his time at Sporting far from a success to date.
Markovic has played 13 times for the Primeira Liga side, scoring twice, averaging just 43 minutes per appearance and making two starts in the league.
The Serbia international was sent to Sporting to rejuvenate his prospects, but instead, another injury serves to reduce his value to Liverpool in the future, with his fate on Merseyside seemingly sealed.
Markovic spent the 2015/16 campaign on loan with Fenerbahce in the Turkish Super Lig, but only played 21 games in all competitions, scoring twice, assisting three times and averaging 57 minutes on the pitch per outing.
He missed the last 14 games of the Super Lig season with a hamstring problem that also kept him out of five Champions League games and four in the Turkish Cup.
Returning to Melwood early in the summer, Markovic looked to prove himself to Jurgen Klopp, and impressed in patches during domestic pre-season games.
But this was clearly not enough for the German, despite a lack of genuine wide players in his squad—something that is becoming more apparent now, with Philippe Coutinho sidelined himself.
Sadio Mane is due to depart for the Africa Cup of Nations in January and, on paper, Markovic would have been an ideal replacement.
But the former Benfica star has proved too unreliable since making the move to Merseyside in 2014, and following this latest layoff, he could be lacking suitors in the summer transfer window.
It remains unclear whether Markovic will return to Liverpool for treatment.