The Chronicle reports that the player is keen to move to St James Park this summer after impressing in both the Championship and the European U21 championships.
Palace had been linked with a move for the player but were unable to convince him to join from Norwich.
Murphy was a Newcastle fan growing up as a young player and is said to be holding out for a move to his boyhood club. The Magpies have already failed with one bid and are expected to go back in with a second bid.
With Frank de Boer taking over at the helm this summer, Palace have been one of the quieter teams in terms of transfer activity.
The club have made just one signing this summer, bringing in fellow England U21 international Ruben Loftus-Cheek on a season-long loan from Chelsea.