The report claims that the Reds have accepted the offer from Fenerbahce despite the defender having two-years remanning on his contract.
Skrtel fell out of favour with recently appointed Liverpool boss Jurgen Klopp and is expected to leave the club after Euro 2016.
The experienced defender joined the Reds for £6.5 million from Zenit Saint-Petersburg in 2008 and has made 320 appearances for the Premier League outfit.
Skrtel will become the second defender to leave the club after Kolo Toure was released after his contract ended.
The report also claims that Skrtel has had offers from China and Germany but Fenerbahce were able to offer a lucrative deal with the prospect of first team as well as Champions League football.
The powerful defender featured in Slovakia’s 2-1 win over Russia in their second Euro 2016 game yesterday.