The Northern Irish international turned down a new contract last month, and he has been linked with moves to Arsenal, Manchester City and Leicester City.
Baggies boss Alan Pardew has reportedly been told he will have to sell players in order to buy in the January transfer window, and it seems the sale of Evans for £25m would be used to sign either Newcastle’s Aleksandar Mitrovic or Watford’s Troy Deeney.
The Gunners look to have a clear run to buy the centre back. Manchester City will likely seal the signing of Aymeric Laporte from Athletic Bilbao very soon, which will mean they will withdraw from the race for the 30 year old.
Arsenal’s chief executive Ivan Gazidis and the club’s transfer negotiating team are said to be focused on signing Borussia Dortmund’s Pierre-Emerick Aubameyang, but with just seven days until the window closes, they will not have much time to make a move for Evans.