England could be willing to wait for a manager such as Arsenal's Arsene Wenger to complete his current contract as the Football Association searches for a manager to replace Roy Hodgson, chief executive Martin Glenn has suggested.

Monday brought the well-travelled 68-year-old's turbulent four-year reign to a shuddering halt, with the shock Euro 2016 exit to Iceland in the last 16 leading to his immediate resignation.

Talk swiftly turned to finding Hodgson's long-term successor, and Glenn would not rule out waiting until the end of the Premier League season should the right person then be available, with Wenger one such high-profile manager whose deal expires next summer.

"It is a possibility, of course," he said when asked if he would be prepared to wait for a contract to expire. "If you said, 'This person is an absolute shoo in, can you wait?' then we are well-placed I think with an interim solution.

"You might get interim solutions plural as we have had in the past -- get a few managers to come and help. It is such an important decision, we have got to get the right person.

"To wait a few months -- if that is what we had to do -- I think would be the right decision."

Glenn was not keen to talk names on Tuesday, but he conceded England under-21 manager Gareth Southgate would be a "pretty obvious" interim solution should they not appoint Hodgson's successor by the first World Cup qualifier against Slovakia on Sept. 4.

"We'll see," he said when asked of the time scale. "We'd like to get one for the first World Cup qualifier, but if we won't we have an interim plan in mind.

"We are not talking about names today, but it would be a pretty obvious one to pick.

"We just don't know yet who the runners and riders would be. We are going to scope out, which we start at the end of this week with [FA vice-chairman] David Gill and [technical director] Dan [Ashworth].

Arsene Wenger will be out of contract at Arsenal next summer, a year before the 2018 World Cup. Getty

"[The question] is, 'What's the problem we need to solve?' We clearly need an inspirational manager who can harness all of the resources that the English game, the big resources, has got, everything we have now got at St George's Park, to make us more resilient in tournaments.

"That I think is a brief, but we want to work that through, but it is an inspirational manager and management team to get the best out of a squad which has got high potential."

Glenn said he would not wait to name Hodgson's permanent successor if he felt it would jeopardise qualification for the 2018 World Cup and conceded it was "unlikely" he would hold off for a whole year, but not inconceivable.

Glenn suggested several people could take temporary control and did not rule Southgate out of the running for the permanent post, nor anyone else.

"As I said, it has got to be the best man or woman for the job," said Glenn. "More likely a man, but it's the best person for the job. I don't think we are ruling out anything.

"An ideal mix is somebody who has had experience of the English game, ideally at a significant level. That is what you would look for."

Such indecision appears borne out of the fact the FA is starting from scratch, with the chief executive saying there was no pre-existing shortlist in order not to undermine Hodgson.

Glenn plans to act as a counter-balance in the triumvirate leading the search for the new boss, which includes Gill and Ashworth, having conceded he was "not a football expert."

The FA chief executive says current senior members of the England squad will be canvassed for their opinion, along with current and former players and managers.

"It's the old joke, 'What's a camel? It's a horse designed by committee'," Glenn said. "You'll have 55 different opinions in this room about who should be manager, but we are going to use the opinions, and wisdom and insight of current managers, former managers and players.

"There's going to be a broader process of consultation."

Gary Neville worked under the outgoing England boss and his role on the coaching staff looked to be succession planning, but his exit with Ray Lewington has seen those odds lengthen.

"I have got to speak to Gary," Glenn said when asked if Neville had made a clean break. "I think he will be part of the process of saying, 'What do you think?'

"He needs a bit of time to decompress. He is distraught about the result last night. Now is not the time to be talking to him. He is obviously a person that you would want to get an opinion from.

"He is very opinionated as you know, so having been close to it he'll part of it. We're not talking names today but you'd want to speak to him about things and see what he says."