The Baggies did well to keep hold in the summer and are reported to have knocked back bids in the region of £25million as Manchester City were sniffing around.
Albion are bracing themselves for more interest in the January transfer window and reports have claimed that new Hammers boss David Moyes wants him on board to help plug a leaky defence.
Whether Evans would consider such a move remains to be seen as it is thought he would prefer to return further north if he did leave the Hawthorns.
That could also open the door for Everton, who are also known to be keen as Sam Allardyce looks to strengthen his newly inherited squad.
Albion boss Alan Pardew will be keen to keep hold but offers in the region of £30million could severely test their resolve.