The 36-year-old last played for Paraguayan club Olympia but left in July after complications due to the coronavirus pandemic.
He is now a free agent and is keen for another shot at the Premier League as he looks to score three more goals and take his tally in the division to 100.
The Sun reports that the Baggies have held talks with Adebayor’s representatives and a deal is very much a possibility with the newly-promoted club desperate to add a striker to their ranks as soon as possible.
The veteran is without a club but has reportedly been training twice a day at his home in Ghana to stay ready for an opportunity when it arises.
He scored 46 league goals for Arsenal, 15 for Manchester CIty and 35 for Tottenham, taking his tally to 97.
After leaving England he had spells with Istanbul Başakşehir and Kayserispor in Turkey before his short jaunt to Paraguay earlier this year.
West Brom have lost their opening two Premier League matches this season and were dumped out of the Carabao Cup by Championship side Brentford.
Slaven Bilic is desperate to sign a striker, but their defence looks in need of improvement as well having conceded eight goals in just two league games.