Tottenham manager Harry Redknapp is the leading contender to lead England into the European Championship in June, but the FA is now willing to allow its new coach to start after the tournament if that is a deal-breaker.
Before any official approach is made, the FA hopes to discover privately whether its preferred candidate wants the job.
FA chairman David Bernstein says "our next step is to narrow that target list down to a very small number of key people who of course we believe actually want the position. There may be other people who don't actually want this position."