The Premier League title contenders have been searching for the German's successor ever since he announced in January that he would be departing Anfield at the end of the season.
Since Xabi Alonso revealed that he would be remaining at Bayer Leverkusen, Ruben Amorim has been tipped to leave Sporting Lisbon for Merseyside.
However, reports emerged on Monday suggesting that the Portuguese was 'unlikely' to move to Liverpool and was instead open to taking the West Ham United job, should it become vacant.
That has thrown open the possibility of an alternative entering the race, Liverpool also said to be admirers of Lille boss Paulo Fonseca.
Liverpool show interest in O'Neil?According to established X account DaveOCKOP, the Liverpool hierarchy have taken the decision to hold talks with Wolverhampton Wanderers head coach Gary O'Neil.
The 40-year-old arrived at Molineux in August tasked with the job of keeping Wolves in the Premier League after Julen Lopetegui had left just days before the start of the season.
Wolves were also heavily restricted in the transfer market by their need to meet the Premier League's Profit and Sustainability regulations.
However, O'Neil has won over his initial doubters by moving Wolves into contention for European qualification until a recent drop off in form, largely due to a lack of available attackers.
Regardless of how Wolves end the season, O'Neil's stock is unlikely to drop in the short term with his side having already delivered 43 points from their 33 Premier League fixtures.
Why O'Neil should not be viewed as a surprise candidateBased on his impact at Wolves alone,
Read on sportsmole.co.uk