The £6 million rated Slovakian looks to be on his way out of Anfield.
Skrtel (R) is set to leave Liverpool after eight years
Aitor Karanka's side boasted the Championship's most watertight defence in 2015-16, but have seen their numbers depleted by the departures of Jonathan Woodgate and Damia Abella at the end of their contracts, along with the loan returns of Ritchie de Laet and Tomas Kalas.
Woodgate is leaving his hometown team following promotion
Turkish giants Besiktas have also been credited with an interest in the former Zenit St. Petersburg stopper, with Sven-Goran Eriksson's Shanghai SIPG another club said to be keen.
Eriksson wants to bring Skrtel to China, the report claims
The report claims that Skrtel stands to earn more money moving abroad, although the stability of staying in the Premier League may also appeal.
Liverpool have already added Schalke's Joel Matip to their ranks this summer, but are releasing Kolo Toure, with Steven Caulker set to return to parent club Queens Park Rangers.
And another centre-back is likely to be sought by Klopp, especially if Mamadou Sakho fails to have his provisional drugs ban overturned.
Matip (R) arrives at Anfield on July 1