The Reds are very eager to bring in the youngster, who is now an England regular.
Guehi is one of many who may depart Palace in the summer, even if they remain in the Premier League.
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Per The Mail, Liverpool are set to lead the way for his signature at present.
However, Manchester United would also be a contender if they get Dan Ashworth in as sporting director.
The current Newcastle supremo has long been linked with making a move for Guehi.