The Tottenham boss is favourite to take the role following the resignation of Fabio Capello earlier this month.
Stuart Pearce will be in charge for England's friendly against the Netherlands on Wednesday, while he has also admitted he would be happy to lad the country through Euro 2012 in the summer.
Bevington would not be drawn into speculation regarding who will fill the position permanently but remained adamant the FA would not rush their decision.
"We haven't spoken to any individual or any club at this stage," Bevington told the BBC.
"We're just ensuring we go about it in the right way and we are certainly not going to knee-jerk into anything.
"I am not prepared to answer any questions on who it may or may not be.
"Obviously we have been talking at length but we have to respect any managers and any clubs during this process and we will do so before we determine the path we want to follow."
Director of football development Sir Trevor Brooking has also suggested there is no need for the FA to rush into a decision, with the quality of the players available allowing a late appointment to be made.
"There's no need to rush into it because we have got a bit of time now before the end of the season.
"Whoever takes them in the summer, the players are of such a quality that they could come in really late and gel them into a good unit so, as I say, let's see how we go."