The 29-year-old scored 11 Premier League goals for last season's FA Cup winners but is set to leave following their relegation to the Championship.
The Magpies face competition from Everton, with Wigan manager Owen Coyle saying the Toffees are the Ivory Coast forward's preferred destination.
"I'm led to believe through his representative that Everton is the club he wants to join," he said on Monday. "It's not rocket science to say that Kone will probably leave at some point this week.
There have been a number of offers in for him. "There is no problem. He goes with our blessing because I need players who need to be at Wigan.
If his heart's elsewhere then he's no good to me." Kone signed a three-year contract when he joined Wigan from Levante last summer and was part of the side that won the club's first major trophy when they beat Manchester City 1-0 to win the FA Cup in May.