Hodgson has taken the first step towards becoming the next England manager after telling West Brom he wants to speak to the Football Association about replacing Fabio Capello.
West Bromwich Albion have confirmed permission has been granted for talks to open.
The move has stunned the English game as Tottenham Hotspurs manager Harry Redknapp was widely expected to get the job.
West Brom chairman Jeremy Peace said: "The club are currently in negotiations with Roy about a new contract - his current deal ends on June 30 - and remain very keen to bring these talks to a successful conclusion. However, Roy has expressed a desire to explore this opportunity and, accordingly, the club have granted him permission to speak to the FA.
"Roy has done a fantastic job over the past 15 months and the fact the FA want to discuss the England role with him is testament to that. However, we have emphasised to Roy how much we would like him to remain as our head coach and continue his major contribution to our project at the Hawthorns as we look to establish ourselves as a Barclays Premier League club."
It is still possible that Hodgson will say no to the England job but that seems unlikely as he has said in the past it would be "a tremendous honour".
With his West Brom contract almost up, Hodgson would command barely any compensation, another factor which may just have helped the FA reach its decision.
FA chairman David Bernstein said: "I'm grateful to Jeremy and all at West Bromwich Albion for their co-operation in allowing us to approach Roy, who I have since spoken with.
"Roy is the only manager we have approached and we remain on course to make an appointment within the timescale we set out soon after Fabio Capello's departure. Further conversations will now take place with Roy and my Club England colleagues before any further announcements can be made."
Hodgson has built up an impressive CV, which includes spells in the international game with Switzerland - whom he guided to the 1994 World Cup and Euro 96, although he resigned before the latter took place - Finland and the United Arab Emirates.
The Press Association, photo: ihughes22