The Netherlands international is under consideration as the Reds draw up plans for the January transfer window.
Jurgen Klopp is keen to bolster his attacking options with Danny Ings out for the season and Sadio Mane likely to be missing for a month after the turn of the year due to his commitments with Senegal at the Africa Cup of Nations.
Promes fits the profile as he’s quick, skilful and is comfortable playing anywhere along the frontline.
The 24-year-old boasts an impressive scoring record of 36 goals in 71 appearances for Spartak since joining them from Twente in 2014.