Draxler, who sealed a move to Paris-Saint Germain from Wolfsburg, was earmarked as a January target Klopp but the German boss refused to pay astronomical wages for any potential new recruits.
Liverpool, set be without Sadio Mane for the entirety of January due to his involvement in the Africa Cup of Nations, will turn their attentions to Spartak Moscow winger Promes after missing out on Draxler.
24-year-old Promes, who has earned 14 international caps for the Netherlands, boast an impressive goalscoring record having notched 37 goals in 72 appearances for Russian club Spartak Moscow.
Promes arrived in Moscow after his €15 million transfer from Dutch side FC Twente and is valued by Spartak at around £20m, according to the Mirror.