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.