The Baggies attempted to sign Cole during the January transfer window, only to have their plans scuppered in the final moments, but a report in London24 claims they could revive their interest in him this summer.
Cole, 31, is out-of-contract at West Ham, and it was confirmed last week that he would be leaving the Boleyn Ground. A hero in East London, the former England international may not been the greatest goalscorer, but impressed with his work rate and desire, and was good at link-up play.
As a free agent, there are worse players Tony Pulis could look at this summer, even if Cole does not provide the consistent goal threat that the Baggies manager is keen to add to his squad.
This report comes days after the Baggies were linked with a free move for another former West Ham attacker, with Brazilian winger Nene linked with a switch to the Hawthorns by the Mail.
A move for Cole makes more sense, as he does provide a goal threat, whilst he is slightly younger, and has a wealth of experience of Premier League football, something Nene cannot bring to the Midlands club.