The Reds are chasing the younger of the Belgian brothers.
The 21-year-old is the younger brother of fellow Blues star and 2014 PFA Young Player of the Year winner Eden and joined the west Londoners at the same time as his sibling in 2012.
Bundesliga outfit Schalke 04 are also thought to be keeping tabs on Hazard as the attacking midfielder’s future at Stamford Bridge grows increasingly uncertain.
Unlike Eden – who was a £32m acquisition from Lille a little under two years ago – Thorgan was a relatively cheap buy from Lens, with the starlet costing around £880,000.
This season Hazard junior has played 50 matches in all competitions for Zulte, scoring 16 goals and providing 20 assists.
Jose Mourinho flew out to Belgium earlier in the campaign to watch the youngster play, but incorporating him into the squad could still prove difficult.
Hazard would have to compete with his brother, Brazilian duo Oscar and Willian, Andre Schurrle and Mohamed Salah for a place in the first team, with a number of other attacking midfield stars also being on-loan currently.
The Reds however, would be able to offer the Belgium international more game time as they look to strengthen their squad upon their return to the Champions League after a five year absence.
Currently the only players at Anfield who play in the same position as Hazard are Philippe Coutinho and Raheem Sterling, with Suso also expected to return to Merseyside after a decent loan spell in Spain with Almeria.
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