The squad are not due back until Saturday, but Paul Joyce of the Express explains that Markovic has already made his return to Melwood, following a season-long loan at Fenerbahace in 2015/16.
The 22-year-old fell out of favour under Brendan Rodgers and by the time Klopp had replaced him last October, Markovic had already been moved on to pastures new.
The Serbian international is clearly a big talent, and his versatility, work-rate and general quality appear to be a well suited for Klopp.
There are lingering doubts though over whether the 49-year-old will retain Markovic’s services, with the German likely to have specific transfer targets already lined up.
The player is showing that he is keen to prolong his stay at Anfield and that kind of dedication is likely to impress his manager.
Markovic scored three goals in 34 appearances in his only season at Liverpool to date, but there was a feeling that he was never really given a fair crack of the whip, having joined for £19.8million from Benfica in July 2014.
Rodgers continually played him out of position, often used as a right wing-back, and he could never get a significant run of first-team action.
Meanwhile, another player set to return to pre-season training is Mario Balotelli.
The 25-year-old is likely to be deemed surplus to requirements, with the club still waiting for firm offers from other clubs, but he has been told he is expected to be present on Saturday.
The thought of Balotelli doing triple sessions is both hilarious and unthinkable in equal measure – you could barely think of a footballer less suited to Klopp’s style of play.