Jurgen Klopp is keen to rebuild his midfield at the end of the season following an underwhelming campaign.
The Reds have been linked with Jude Bellingham for several transfer windows.
But reports this week claim they have pulled out of the race for the England international, 19.
And now Sky Sports have stated that Gravenberch, 20, is on Liverpool‘s shortlist of alternative options.
The Dutch youngster only joined Bayern from Ajax last summer for £16million.
But he has started just four games in all competitions this season and could already be looking elsewhere for game time.
Liverpool are said to have sought discussions with Gravenberch’s management ahead of a move for the Amsterdam-born star.
Speaking recently to Ajax Showtime about his first season with the German champions, he said: “Ideally, I would like to be successful at Bayern.
“But if that doesn’t work out and I don’t get a chance, then I might have to look around.
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“At the moment I’m not thinking about it and I hope that I can change my situation at Bayern by training and playing well.”
He went on to add: “For me, this season is just the first season where I’ve been struggling and not being able to play much. As a player, you also get better through such experiences.
“I’m still very young and I’m glad I’m experiencing something like this now and not later in my career.”
Alongside his promising club career, Gravenberch has already been capped 11 times by the Netherlands.
However, he did not make Louis van Gaal’s squad for the 2022 World Cup.
Meanwhile, Liverpool are set to miss out on Champions League football next season.
Klopp’s men sit eighth in the Premier League table, 12 points adrift of the top four with just nine games remaining.