The 64-year-old was the FA's surprise choice to replace Fabio Capello as England manager and Willie Duncan looks at who might succeed him as Baggies boss next season
Hodgson, who was named as successor to Fabio Capello last week, will take charge of his former club for the final time on Sunday when Arsenal visit the Hawthorns before taking over the England hotseat.
That, of course, means that a new manager will take over at West Brom next season and William Hill have opened a book on who will replace Hodgson as the next permanent boss of the Baggies.
The strong favourite for the post at this stage appears to be a face which will be familiar to fans of English football - Claudio Ranieri.
The former Chelsea manager was sacked by Inter back in March and it is believed that Ranieri would welcome the opportunity to return to the English Premier League.
Subsequently, Ranieri and West Brom might just be a perfect fit and the Italian manager is a 4/7 (1.57) shot to take charge at West Brom.
Former West Bromwich Albion first-team and caretaker coach Michael Appleton, currently in charge at recently relegated Portsmouth, is next in the betting at 4/1 (5.0) as is Birmingham City boss Chris Hughton.
Appleton, 36, played for West Brom until 2003 when his career was ended by a knee injury but the manager's post may be too big a step up while Hughton is unlikely to entertain an offer from the Baggies unless Birmingham are unsuccessful in their attempt to gain promotion to the Premier League via the Championship play-offs. Should the Blues fail, though, the former Newcastle United boss would be a lively contender at 4/1 (5.0).
Arguably, the most interesting name at the top end of the betting market is that of Tony Mowbray. Mowbray was in charge of West Brom from 2006 until he left the club to take up the post at Celtic in 2009. A return to the Hawthorns for Mowbray is rated as a 6/1 (7.0) with William Hill.
Hodgson has helped to establish West Brom as a Premier League club this season, with a top half finish still in sight with one game to go, and whoever succeeds the new England boss in the Hawthorns hotseat will face the task of building on his considerable achievements.
Next permanent West Brom manager:
Claudio Ranieri - 4/7 (1.57)
Michael Appleton - 4/1 (5.0)
Chris Hughton - 4/1 (5.0)
Tony Mowbray - 6/1 (7.0)
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Willie Duncan is a freelance sports journalist. Willie, from Edinburgh, has covered Scottish football for over 10 years and he specialises in football betting markets from across Europe. You can also follow Willie on Twitter here.