The FA is seeking a new England boss after Sam Allardyce left the position on Tuesday, following a sting by the Daily Telegraph newspaper, having spent just 67 days in the job.
Davies, who spent more than a decade at the FA, believes Wenger would be a perfect replacement and England should appoint a caretaker until the Frenchman's contract with Arsenal runs out in the close season.
"I would like to be confident he (Wenger) had been asked, quite straightforwardly, if he would like to be England manager in the near future," Davies told Reuters on Wednesday.
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"Not next week, or at Christmas, but when his contract ends, as he would like to fulfill it. They can have a caretaker until then, perhaps Gareth Southgate with an experienced assistant."
Having worked with several England managers, from the youthful Glenn Hoddle to the seasoned Terry Venables, Davies believes the position is more suited to an experienced man such as the 66-year-old Wenger.
"There are a number of very strong candidates but my instinct tells me they would tend to be the more experienced people," he said.
"It can be a hugely frustrating job, not least because of the gaps between matches. Would Arsene find those gaps frustrating? I don't know the answer to that question -- I only know him a little."
Davies is more certain about the attributes of Wenger, who has spent two decades in English football and produced several attractive and successful teams, notably the 'Invincibles' who went unbeaten throughout the 2003–04 Premier League season.
"Arsene knows the English game better than anyone after all the years at Arsenal," added Davies, who was attending the Soccerex Global Convention in Manchester.
"He would bring many qualities. Firstly, everybody loves Arsene Wenger's teams. You don't have to be a supporter of Arsenal to like watching his teams play.
"Secondly, he is a very shrewd tactician and understands the mentality of the team ethic.
"Now the problem is always... the difference between club football and tournament football; England have not mastered that in recent times.
"Could Arsene master that? It would be for us to see, but he is one of the best prepared managers around. He understands the marginal gains and the little extras that make the difference."
Davies, who ended the reign of Hoddle in 1999 after the then England manager made disparaging comments about disabled people in an interview, believes it was inevitable Allardyce had to step down.
"You've got to be sad that someone who had dreamed of the job lost it in 67 days but he has said himself it was unwise, to put it mildly.
"Sam talked himself out of the job... It was, I fear, inevitable, because you cannot do that in a job that has a level of scrutiny up there with the royal family."
(Editing by Toby Davis)
