Former FA chief executive Mark Palios does not believe the talks with Hodgson necessarily rule out a move for Redknapp. He said the FA is "under pressure" to do something about the vacant job with Euro 2012 a matter of weeks away.
"Hodgson is a candidate they would naturally speak to," he told the BBC.
" West Bromwich Albion's season is settled and they are now safe. But this doesn't mean to say there aren't other people they would approach."
Hodgson, who had a disappointing time at Liverpool last season, has steered West Brom to mid-table in the Premier League.
And Albion chairman Jeremy Peace remains hopeful he will stay on at the Hawthorns.
Peace said: "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.
"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."
England have two fixtures before their Euro 2012 opener against France on 11 June, with friendlies planned against Norway on 26 May and Belgium on 2 June.
Stuart Pearce - who is in charge of both the England Under-21 squad and the Team GB Olympic set-up - is currently in temporary control of the national side and oversaw a 3-2 friendly defeat by the Netherlands at Wembley last month.