The 64-year-old met with a four-man panel after being given the all clear by his club to hold talks with the FA on Saturday, and is the only name in the frame for the job.
The FA has said that Hodgson is the only person it has approached regarding the job ahead of the European Championships in June.
The four-man panel that will make the final decision over who succeeds Fabio Capello are David Bernstein, FA general secretary Alex Horne, FA director of football development Sir Trevor Brooking and managing director of Club England Adrian Bevington.
Harry Redknapp has been touted by many as the favourite for the role since the departure of the 65-year-old Italian in February, but the FA decided not to contact the Tottenham manager.
One of the concerns the FA is said to have had over the Spurs boss is whether he shared their vision for the National Football Centre in Burton, designed as a £100 million centre of excellence for coaching.
Hodgson's contract with West Brom ends on June 30, and it is expected that he will be offered a long-term deal that will span to Euro 2016.
The Baggies manager has extensive international experience, beginning his managerial career at Swedish side Halmstad in 1976, and has since managed the national sides of Switzerland, United Arab Emirates and Finland, as well as domestic sides in Italy and England.
Regarding speculation that the FA planned to appoint a successor in the coming week, Hodgson recently told BBC Radio 5 Live: "It's news to me."
"I shall just watch like everyone else interested in football to see who the next England manager will be.
"I don't know what the plans are of the FA, as I've said all along. They've got a job to do. I'm sure they have looked into the sort of candidates that they consider potentially right for the job.
"No doubt, if you say next week, we'll find out which candidate they have plumped for."
The former Liverpool manager has successfully guided West Brom to a comfortable position in the table and to a record third season in the Premier League, while Albion chairman Jeremy Peace remains hopeful that he will stay on at the Hawthorns.
"Roy has done a fantastic job over the past 15 months and the fact the FA wants to discuss the England role with him is testament to that," he enthused.
"Roy is a proud Englishman and we can understand why he wants to speak to the FA about this highly prestigious managerial position.
"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 Premier League club.
"Everyone here has an excellent working relationship with him and he is immensely popular with our supporters."
|"Roy is a proud Englishman and we can understand why he wants to speak to the FA"
- West Brom chairman Jeremy Peace
Stuart Pearce had been in temporary charge of the national side while the FA made their decision, and recently stated that he would be prepared to lead the team at Euro 2012, despite also being responsible for the England Under-21 side and Team GB at the Olympics.
England have only two fixtures before there Euro 2012 opening game against France on June 11, having planned friendlies with Norway and Belgium on the May 26 and June 2, respectively.