Everton - and Roebrto Martinez - are believed to be in pole position to land the Ivory Coast international but Newcastle have also been given permission to speak to the player.
He has a £5m buy-out clause in his contract and is looking to activate that following Wigan's relegation in May.
Kone arrived at Wigan from Spanish cub Levante last summer and impressed under Martinez, scoring 11 league goals.
Alan Pardew is keen to strengthen his attacking options after Demba Ba's January departure for Chelsea with St Etienne's Pierre Emerick Aubameyang and Aston Villa's Darren Bent both being linked.
Newcastle United have completed the signing of midfield prospect Olivier Kemen, 16, from Metz while youngsters Paul Dummett, Conor Newton, Jak Alnwick, Jonathan Mitchell, Michael Richardson and Alex Gilliead have all signed new deals.