The Serbia international midfielder joined the Reds in January 2016 as a highly-rated prospect.
He has, however, been restricted to just 13 appearances and is yet to start a Premier League fixture.
The 21-year-old’s agent believes that he should now be looking to secure a switch elsewhere when the transfer window re-opens, but only if another opportunity in England can be found.
Zoran Stojadinovic told Serbian publication Blic: "Grujic has to go somewhere in January in a loan, in a team where he will play.
"It must be an English club, so as not to make a mistake like Lazar Markovic did.”
Grujic’s fellow Serb, Markovic, also struggled to make an impact at Anfield following a high-profile move from Benfica.
"Had Lazar been my client, I would never advise him to leave England," Stojadinovic added.
"He changed the country, the style of football, the temperament, the climate, and therefore his return to Liverpool was an impossible mission.
"To return to Grujic, he is very much appreciated in Liverpool and therefore he did not go anywhere because they did not want to let him go.
"But he needs more minutes in the field and that's why the loan is the best solution for him in January to return to Liverpool after his return to the starting line-up."
Grujic has made one start under Jurgen Klopp this season, in a Carabao Cup clash with Leicester, with four other outings – in the Premier League and Champions League – all coming as a late substitute.