The Slovakia captain, 31, played 319 games for the Anfield club since signing in 2008 and completed a medical with Fenerbahce on Wednesday.
Skrtel apologised recently after appearing to support an insult of manager Jurgen Klopp on social media.
Another player likely to leave Anfield is striker Mario Balotelli, who Klopp has told to find a new club.
Liverpool defender Martin Skrtel has completed his move to Turkish side Fenerbahce for a reported £5m.