King joined Everton on the last day of the winter transfer window this year on a deal that ran through until the end of the season.
He made eleven appearances for the Toffees in the past season in the Premier League, but failed to score a single goal or record an assist.
Everton decided not to extend King’s stay at Goodison Park and instead released the player, rendering him a free agent.
King was targeted by the Magpies in the last summer transfer window when he was still at Bournemouth, but the transfer did not come to pass.
Newcastle have set their sights on the forward again and it is claimed will hold formal talks with him over the next few weeks.
If signed, King would join his former Bournemouth team-mates Ryan Fraser, Callum Wilson and Matt Ritchie at St. James’ Park.
Magpies boss Steve Bruce’s intention with the potential transfer would be to bring a player with plenty of experience in the Premier League, with King having made over 170 appearances in the top flight, and add to his side’s goal threat.