The 32-year-old has one year left on the two-year deal he signed on joining the Baggies last summer following his release by Manchester City.
Villa have been active in the transfer market since offloading star striker Christian Benteke to Liverpool for £32.5m.
Tim Sherwood is keen to bolster his squad and, after completing the signing of forward Jordan Ayew from Lorient, he is closing on deals for Emmanuel Adebayor from Tottenham, Rudy Gestede from Blackburn and Nantes midfielder Jordan Veretout, with the trio soon to undergo medicals at Villa Park.
Veteran Dutch defender Ron Vlaar’s contract with Villa has expired and Sherwood is in the market for an experienced replacement.
Former England defender Lescott made 29 appearances in his debut season at the Hawthorns but there may be more competition for a centre-back spot next season following the arrival of James Chester from Hull City for £8m.