The Express & Star revealed earlier this month that both Chris Wilder and Frank Lampard have been shortlisted for the role.
Both men are believed to be keen on the job and the chance to mastermind a promotion push with Wilder currently the odds on favourite with the bookmakers.
But according to reports, Hodgson is another boss the Baggies have shortlisted in a move that would see the 73-year-old make a sensational return to The Hawthorns.
Hodgson was named Baggies boss in February 2011 and enjoyed 18 successful months at the club before being appointed England manager.
Earlier this month, he left Crystal Palace after his contract expired – with the former Inter Milan chief having spent the last four seasons as Selhurst Park.
And Hodgson has made it clear he isn't yet ready to retire from football with the vastly experienced head coach believed to be open to the idea of returning to management.
The Baggies are on the hunt for a new boss after Sam Allardyce opted to leave the club following relegation back into the Championship.
Alongside the Dudley-born chief, coaches Sammy Lee and Robbie Stockdale also left the club.
And that means any new manager will also be able to bring in his own backroom team – with Hodgson believed to want to continue working with long-time assistant Ray Lewington if he is going to accept another managerial role.
Alongside Hodgson, Barnsley's Valerian Ismael is another manager to be linked with the head coach role at The Hawthorns.
But the Baggies would have to pay £1.5m in compensation if they were to appoint the Frenchman.
Despite the links to Hodgson and Ismael, it is believed Wilder and Lampard remain the front runners for the role.
The Baggies hierarchy, however, felt it was important to carry out a thorough recruitment drive as they look to return to the Premier League at the first attempt.
Meanwhile, Albion's Callum Robinson has withdrawn from the Republic of Ireland squad that is due to take on Andorra on Thursday and Hungary on Sunday.
The Baggies forward has pulled out after picking up an Achilles injury.