The midfielder made two Carabao Cup appearances for the Reds this season before Jurgen Klopp’s side were eliminated by Arsenal on penalties last week, and those outings marked his first for the club since December 2017.
The Serb has spent the last two seasons on loan at Hertha Berlin.
And another Bundesliga side are eyeing Grujic, with Liverpool keen to avoid sending him on loan again, preferring a permanent transfer away from Anfield for the 24-year-old.
Werder Bremen are interested in the midfielder, PA has reported, with Xherdan Shaqiri another Liverpool player who could depart on deadline day.
Information from PA contributed to this report.