The 31-year-old Lescott was reportedly close to signing a deal with Hull City, and the club was ‘optimistic’ about their chances of landing the Midlands-born defender.
Now, however, it appears Lescott prefers with new Baggies manager Alan Irvine, with whom he worked at Everton.
Several teams, including Stoke City, have shown an interest in the England international since Man City announced they had released him after five seasons.
Lescott has been playing professionally since 2000, when he joined Wolverhampton. He then left for Everton in 2006 before arriving in Manchester in 2009. Overall, he has played in 432 league matches with the three clubs, amassing 34 goals in that time period.
He also has 26 caps for England, most recently receiving two in 2013.
Lescott had seen his playing time decrease dramatically in the last few seasons, appearing in just 10 Premier League matches with the club.