The Turkish transfer window closes on midnight on Friday, and Markovic is said to be “ready to return” to the Istanbul club, where he spent 2015/16 on loan.
Now, according to the Liverpool Echo, the Reds “do not expect the Serbia international to depart.”
The 23-year-old is therefore “set to remain a Liverpool player until at least January.”
Whether he will be involved in the first-team remains to be seen, with Klopp only using him in the first pre-season friendly at Tranmere this summer and not featuring in the squads for the Reds’ trips to Hong Kong or Germany.
Markovic could feasibly be called upon in cup competitions, with Klopp required to rotate to keep his first-team options fresh.
Sheyi Ojo had already joined Fulham on a temporary basis, with Klopp sanctioning the departures of three wide options.
But Markovic could well be required at times, particularly if Liverpool remain in both cup competitions.
Having Markovic available to deputise would be useful, as the Serb does possess the raw qualities needed to operate in one of the wide roles in Klopp’s forward line.
There have remained question marks over his work rate and commitment in training, however, so he will face a fight to convince Klopp his long-term future remains on Merseyside.