Earning plaudits for his loan spell at Hertha Berlin in the season just gone, the 22-year-old has drawn admirers in the Bundesliga and beyond.
Now, Aksam are claiming the Super Lig champions want to plan a way to prise the Serbian midfielder from Anfield with a loan deal and have been scouting him for the past three years.
Unlike some of the sides linked with Grujic, the Istanbul side can offer him Champions League football, which could be a big pull factor if their attempt to convince Liverpool come off.
At the helm of Turkey’s most successful domestic club, Fatih Terim is apparently eager to work with Grujic – a player they have previously been linked with on a loan move basis.
Aksam, however, also report Galatasaray will have to fend off interest in the Serbia international from Bundesliga clubs Frankfurt and Werder Bremen, as well as La Liga heavyweights Atlético Madrid.
With a contract that runs for another four years, his future is safe at the Reds should we decide to keep him permanently but ship him out on loan again.
Jürgen Klopp’s first-ever signing at Liverpool, Grujic has been a victim of our new midfield wealth.
If we decide not to cash in on him, perhaps a place could open up for Grujic as an option when the evergreen James Milner eventually hangs up his boots?