The 26-year-old Senegalese star has scored 18 goals and made eight assists in 41 appearances for the Super Lig club, since signing for last season's runners-up in Turkey for €10million in January last year.
Sow was a reported Liverpool target when he left Ligue 1 Lille at the turn of 2012, before opting instead to move to Istanbul, where he signed a four-and-a-half-year deal with Fenerbahce.
Only last year, the African forward went on record saying he would relish the opportunity to link up with the Anfield club, saying: "I want to play in England one day. Liverpool, well, that is a dream club. Anyone would be happy, scoring goals in front of the Kop can be the highlight of a career."
Reds boss Brendan Rodgers has already added to Liverpool's forward line, with the January acquisition of Daniel Sturridge from Chelsea. However, there is a chance that the Premier League club could be in the market for another forward, in a bid to relieve some of the goalscoring pressure on Luis Suarez.
Liverpool have endured something of a striker shortage since summer signing Fabio Borini was injured on international duty, prompting academy product Raheem Sterling to be fast-tracked into the first-team.
The talented teenager was already starting to make his breakthrough on Merseyside, but would have likely been given a little more protection, and time to find his feet, had Rodgers' squad not been hit by injury.