Championship outfit Middlesbrough have shown interest in signing the 32-year-old as well, but according to the Guardian, he has rejected the chance to link up with Tony Pulis.
Puncheon has a contract at the club till 2019, so Newcastle can expect to get him on a relatively cheap deal. He would not be the most high profile signing that the Magpies fans want to see but given their financial plight, Benitez has few options left with him.
Will it be a good move?
Since joining the club in 2014, Puncheon has been a regular and key player for Palace, until last season. He lost his place in the starting XI after the arrival of Roy Hodgson and then suffered a season-ending injury in January, making only 10 Premier League appearances in 2017-18.
However, he is an experienced Premier League attacking midfielder and the former Southampton player can provide creativity to the side.
It has been an underwhelming transfer window for the Magpies and Benitez is facing a race against time to bring in new faces before the transfer window slams shut in a few hours from now.