Grujic has spent the last two seasons on loan in Germany at Hertha Berlin and is expected to leave Liverpool before the transfer window slams shut.
He has attracted interest from several clubs and could even have rejoined Hertha Berlin, but the capital outfit are signing Matteo Guendouzi on loan from Arsenal.
Grujic could still return to the Bundesliga though as, according to German daily Bild, Werder Bremen are moving to sign him.
The German side are moving to capture the Serbian midfielder on a loan deal.
Liverpool have been looking to sell Grujic and it remains to be seen if the loan agreement contains any option for Werder Bremen to sign him on a permanent basis.
The 24-year-old is down the midfield pecking order at Liverpool and if he does not move then his chances of first team football look bleak.
Grujic, who has also been linked with West Ham, is well regarded in the Bundesliga following his spell at Hertha Berlin.
