The former Liverpool boss has previous experience at international level after spells with Switzerland, UAE and Finland with his current deal set to expire at the end of the season
FA chairman David Bernstein revealed the news in a statement on the governing body’s official website, revealing the 64-year-old is the only candidate to have been approached, even though Tottenham's Harry Redknapp had been considered as the favourite for the role.
Hodgson's current deal at the Hawthorns is up for renewal at the end of the season.Bernstein said in the statement: "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 experience managing at international level after spells with Switzerland, UAE and Finland.
Arguably the two most high-profile clubs the Baggies boss has coached are Inter and Liverpool.
West Brom released a statement confirming the agreement, while revealing that their own negotiations with Hodgson regarding an extension to his deal have also started but that the manager was keen to hear the FA's proposal.
The statement read: "West Bromwich Albion have today received an official approach from The Football Association to speak to Head Coach Roy Hodgson about the England Manager's post.
"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."
Baggies chairman Jeremy Peace, who initially discussed the terms of the approach with the FA, added: "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.
"Roy is a proud Englishman and we can understand why he wants to speak to The FA about this highly-prestigious managerial position.