Hazard, the younger brother of Chelsea forward Eden Hazard, will enter the final year of his contract at the end of the season and has no intention of renewing his deal.
Jurgen Klopp’s side have been regularly linked with a move for the Belgian, who has scored 11 goals for the Bundesliga outfit this season.
Club director Max Eberl admitted he could end up at Anfield, but also hinted at interest from Borussia Dortmund and Atletico Madrid.
"Thorgan has informed us that he doesn't want to extend his contract and that he wants to leave the club in the summer to take the next step,” Eberl told Sky Germany.
“I've heard this statement 15 times in the last 10 years as really great players have left us. That's the way it is for us.
"We'll have to see where his path will continue. I don't know whether it will be at BVB, who are constantly being mentioned, or at Atletico Madrid, Liverpool or another club.”
Eberl previously told his club’s official website that the €40 million-rated winger won’t be allowed to leave on a cut-price deal.
"Interested parties have to offer us a transfer fee that recognises his worth as an exceptional Bundesliga forward and a regular feature in one of the best national teams in the world," he said.
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