Jurgen Klopp's side have been linked with the 26-year-old attacking midfielder, the younger brother of Chelsea's Eden Hazard.
It has been reported that Liverpool have already bid £36million (€42m) for the Belgian ace.
Hazard has also been linked with Atletico Madrid and Borussia Dortmund.
And the race is on after Hazrad told Borussia Mönchengladbach sporting director Max Eberl that he wants to quit the Bundesliga club this summer.
Gladbach were keen to extend Hazard's contract, which runs until 2020, but the 26-year-old has turned down the offer as he wants to take the next step in his career.