Skrtel has found it hard to re-establish himself in the side following a hamstring injury in December.
Skrtel has fallen down the pecking order at Anfield ever since he picked up an injury in the 3-0 defeat to Watford in September.
Since then he has made just two appearances. He made a forgettable substitute appearance at half-time in the 3-2 defeat to Southampton, after the Reds were 2-0 up, when he had a hand in the Saints' fightback and conceded a penalty, and in the 4-1 win over Stoke City last Sunday.
Skrtel was also omitted from the match-day squad entirely for Sunday's 2-1 win over Bournemouth at the Vitality Stadium despite manager Jurgen Klopp making 10 changes to the side that beat Borussia Dortmund 4-3 in the Europa League on Thursday. Lucas Leiva partnered Kolo Toure at the heart of the defence instead.
Klopp seems to like the centre-back partnership of Dejan Lovren and Mamadou Sakho for the time being, who have presided over some defensive solidity in recent months, although it has not been perfect.
One thing for Skrtel to also take into account is the arrival of Joel Matip in the summer from Schalke, who is also likely to challenge for place in the starting XI. If Lovren and Sakho are ahead of him in the pecking order, and Klopp wants to look at Lucas as a centre-back ahead of next season, then maybe the Slovakian is wise to look for a move elsewhere.
ESPN's report, citing a source, says that a number of Premier League clubs - and some from abroad - are monitoring the 31-year-old's situation.
Given that he signed a new contract in the summer, one would expect that he would command a decent fee if he were to leave the club, and swelling the transfer kitty at Anfield just a little.