The Egyptian defender joined the Baggies on a season-long loan from Al Ahly during the summer transfer window and has immediately impressed starting all 15 Premier League games under Tony Pulis and the newly appointed Alan Pardew.
Jurgen Klopp is desperate to sign a defender to plug Liverpool's leaky defence and has been linked with a number of players since the summer. The Reds have conceded 19 goals in 15 Premier League games thus far and have the poorest record along with Arsenal among the top six clubs.
Liverpool were heavily linked with a move for Southampton's Virgil van Dijk in the summer and looked favourite to land the Dutchman ahead of other interested clubs. But failed with a move and were forced to issue an apology after being accused of tapping up the Saints star.
The German coach is continuing his search for a centre-back and has turned his attention towards the Egypt international, who has impressed despite it being his debut campaign in the Premier League. Hegazi is rated at $5m (£3.7m), but the defender's parent club have made it clear that Liverpool will not be allowed to bid higher in the hope of beating West Brom to his signature.
Abdel Hafiz, the Egyptian Premier League club's manager, has made it clear that the Baggies have the first option to make his loan move permanent and the price will remain unchanged even if Liverpool offer more than his current valuation.
"West Bromwich Albion have the priority to acquire the services of Hegazi on a permanent basis," Abdel Hafiz said, as quoted by Goal.
"If they want to buy him they have to pay $5 million.
"Liverpool do not have the right to bid higher than West Brom because the player is on loan with the Baggies and they do not need to enter new negotiations," the El Ahly coach added.