Following Southgate’s refusal to take that role, they are now seriously considering offering it to Glenn Hoddle, 58, who was sacked in February 1999 over bizarre claims disabled people were paying for sins in a previous life.
The FA are prepared to ask him to take charge while they find the man they want on a long-term basis, even if that is not Wenger, although it is uncertain if Hoddle would be prepared to take it on those terms.
Wenger is expected to met the FA personally to talk about the possibility of taking over, but the prospects of him being swayed are said to be minimal.
As well as the pressures and intensity of the job, the 66-year-old is also understood to be concerned about the whole set-up at the FA.
Being appointed boss would also affect his work at a football pundit on French TV, something he does during international breaks and at tournaments.
As well as the FA three-man panel and senior players it is also understood the advice of another panel – which includes cycling coach Dave Brailsford and former England rugby head coach Stuart Lancaster – is also being sought.