The midfielder, who joined Gladbach from 1860 Munich four years ago, is highly rated and has three caps for Germany.
According to Bild, Borussia Dortmund and Bayern Munich have been keeping tabs on his progress recently, but neither are prepared to commit to a deal as yet, potentially clearing the way for Liverpool.
Jurgen Klopp is known to want to refresh his squad this summer after an underwhelming and injury-hit season, which saw him admit defeat in their quest to retain the Premier League title.
That need for reinforcements will be enhanced by the expected departure of Georginio Wijnaldum, who is out of contract at the end of June.
Neuhaus is a similarly energetic, all-action midfielder and could help to fill the void left by Wijnaldum, who is currently free to discuss terms with foreign clubs.
At 23, Neuhaus is substantially younger than Liverpool’s other senior midfielders and will surely develop further over the coming years.
He made his international debut against Turkey in October, scoring his side’s second goal in an entertaining 3-3 draw.
Gladbach recently confirmed that their manager, Marco Rose, will be taking over at Dortmund at the end of the season and have a fight on their hands to keep hold of Neuhaus.
The two clubs face each other in the quarter-finals of the German Cup tomorrow, with recent events having added an extra dimension to the game.
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