The former Chelsea midfielder has struggled for game time this season, and has so far made just two substitute appearances for the Reds in the Premier League, playing a sum total of just 34 minutes.
Cole appears destined to leave Liverpool sooner rather than later and according to reports in Russia, has an offer on the table from Spartak Moscow.
Moscow boss Unai Emery was keen on taking the former England midfielder during his spell in charge at Valenica, but couldn’t get the deal done with the Anfield club.
However according to Izvestia, West Ham are in the mix and are hopeful of taking the 30-year-old back to his former club.
Cole has endured a torrid time since arriving at Anfield in 2010, and was farmed out on loan to Lille last summer.
Rodgers has moved quick to sell players who don’t appear to fit into his style of play like Andy Carroll – who is on loan with the Hammers – and it appears Cole falls into that category.