Centre-back Lescott, 31, is out of contract this summer after five years with Manchester City.
At his official West Brom unveiling press conference on Wednesday, manager Alan Irvine said: "There is an interest in Joleon, without a doubt.
"He is a player I know well - I obviously had a number of years with him at Everton.
"I've had a great working relationship with Joleon in the past. Coincidentally, I saw him towards the end of the season when Manchester City played Everton and I had a chat with him then - of course, I didn't know any of this was happening at that particular time.
"I believe negotiations are going very well at this particular moment. So hopefully we are able to meet Joleon's demands."
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