The Serbian midfielder has spent the last two season on loan in the Bundesliga with Hertha Berlin, catching the eye with his performances.
It had been thought that the 24-year-old would be on the move away from Liverpool again in the ongoing transfer window, but he is now set to stay put.
“Liverpool want to keep Marko”, the midfielder’s agent Fali Ramadani was quoted as saying by German outlet Fussball Transfers.
“That could change in January at the earliest”, he added.
Hertha Berlin have been keen to re-sign Grujic before the transfer window closes on 5th October, but they may now have to abandon their attempts to take him back to Berlin.
Grujic has another three years left to run on his contract and was Jurgen Klopp’s first signing as Liverpool boss in early 2016.
Klopp now appears to want to look at Grujic over the first half of the season before deciding what to do with him.
Liverpool could still be tested with offers for Grujic, who also has suitors in Italy, before the window closes and it remains to be seen if they change their stance on the midfielder.