TMW says Liverpool are planning to try and land Promes.
The Reds were keen on the 25-year-old last year but a deal failed to materialise.
Jurgen Klopp and co are now plotting a deal to bring the Dutchman to Anfield.
Klopp said of the Dutch attacker last month: "He's a good player, a very good player but there's nothing else to say. There are a lot of good players that we have already.
"We already have a Dutch player (Gini Wijnaldum) who knows him really well so obviously they are good friends but this is not the place to talk about this.
"He's a good player but a Spartak player."