The German international, who is yet to play for the national team at Euro 2020, was one of the standout performers in the Bundesliga last season, and he is now believed to be considering his options.
According to the Liverpool Echo, Jurgen Klopp is monitoring the 24-year-old and will wait until the end of Euro 2020 before he considers making a move, although his addition is not currently one of the club's priorities.
The report also states that Neuhaus had a £34.2m release clause in his contract, but that expired at the end of May.
With Georginio Wijnaldum joining Barcelona when his contract expires later this month, Neuhaus is understood to be one of the leading contenders to replace the Dutchman at Liverpool.
Neuhaus made 45 appearances in all competitions for Monchengladbach during the 2020-21 campaign, scoring eight goals and providing eight assists. body check tags ::