The 20-year-old joined Bayern from Ajax last summer but has endured a frustrating season, having started just once for the Bundesliga giants.
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That led to Gravenberch issuing a warning to Bayern over his lack of playing time.
Bayern are reportedly reluctant to offload the midfield ace but that hasn't stopped the Premier League duo from showing their interest.
According to journalist Fabrizio Romano, Liverpool have held 'direct' talks with the Dutchman as they turn their attention elsewhere after pulling out of the race to sign Jude Bellingham.
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But United remain interested in the midfielder who played under boss Erik ten Hag during their time together at Ajax.
"There is a lot of interest in Ryan Gravenberch. He is not playing for Bayern and he has confirmed he is not satisfied at all, he wants more minutes, and he says that next season it has to change," Romano told Caught Offside.
"There will be a meeting soon between Bayern and Gravenberch, but from the club's perspective, they want to keep him, and have no intention to negotiate for him to leave.
"There has been interest from the Premier League since January - Liverpool, Man United and Arsenal were all informed on his situation but it was not possible to proceed because of Bayern's stance.
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"Liverpool especially remain interested and had a direct conversation with his agent a few days ago, so they are waiting to see if the situation could change."
He continued: "Bayern Munich want to keep the player, but they will discuss his future soon, and we saw last summer with Robert Lewandowski that, even if a club doesn't want to sell, if a player wants to move a deal can happen."
Bayern paid a bargain £16 million for the midfielder who missed out on the Netherlands squad for the 2022 Qatar World Cup.