The centre-back has endured a frustrating start to his Albion career following his move from Manchester City, having being troubled by a knee problem.
Lescott came through a behind-closed-doors friendly against Hull City on Tuesday, though, and head coach Alan Irvine has revealed that the 32-year-old could be in contention to face Roberto Martinez's side at The Hawthorns.
"Joleon played the 90 minutes [against Hull] and played well – he looked good," Irvine told the club's official website.
"Now we will see how he feels after the game but it was very encouraging.
"Now it is really important that we do not rush him because that could lead to a set-back.
"He's got to be right before we consider him for a first-team game but I’m sure he would love to play at the weekend.
"Certainly, the sooner we have Joleon and indeed all the other injury-affected players fit the better."
Fellow new boys Sebastian Blanco and Cristian Gamboa played 90 minutes and 80 minutes respectively on Tuesday, as they build up match fitness and look to force their way into contention.
Albion are waiting to discover the extent of a hamstring injury sustained by midfielder Youssouf Mulumbu on international duty with the Democratic Republic of the Congo, but revealed that Ben Foster, Gareth McAuley and Graham Dorrans are on the mend.
