Eddie Jones and Wayne Smith - two potential leading candidates to succeed Stuart Lancaster as England head coach - have distanced themselves from the role.
While South African Jake White, who masterminded the Springboks' 2007 World Cup triumph, remains a clear bookmakers' favourite, Australian Jones and New Zealander Smith have also been strongly backed.
Jones took Australia to the 2003 Rugby World Cup final, when they were beaten by Sir Clive Woodward's England after extra-time, and he inspired a memorable 2015 World Cup campaign for Japan that included toppling South Africa in scintillating fashion.
Jones, 55, was unveiled as head coach of Cape Town-based Super Rugby franchise the Stormers on Thursday.
Speaking during a press conference after being asked about the England vacancy and reported by www.Supersport.com, Jones said: "Never believe what you read in the papers, mate.
"I am wholly committed to the Stormers.
"When I wake up in the morning I look out on to Table Mountain and think of how lucky I am to be here. This is a fantastic city, and Western Province is one of the most prestigious unions in world rugby, with 125 years of history behind it.
" I feel privileged to get the chance to coach the Stormers. It is my aim to produce a really good rugby team that can deliver on the expectations of the fans. That is my goal at the moment."
Smith, meanwhile, plans to take a a break from rugby after being part of the New Zealand coaching staff that oversaw World Cup final glory at Twickenham just 12 days ago.
"I am being clear with everyone that I'm not coaching full-time in 2016," Smith, 58, told the BBC.
"I've had 29 years in the game as a coach, and it's time for a break. I will see what 2017 and beyond brings."
Rugby Football Union chief executive Ian Ritchie has declared that the search is on for a new boss of "proven international experience", which would appear to suggest the overseas market will be England's stopping point.
The likes of current Australia coach Michael Cheika, Wales boss Warren Gatland and ex-South Africa chief Nick Mallett have also been backed in some quarters as England possibilities.
But while England could now see a first foreign head coach installed after Lancaster departed his role on Wednesday -following a dismal World Cup campaign that produced a painful pool stage exit - the contentious overseas player selection policy is set to stay.
It is understood that there are currently no plans to change England's approach. It remains with an "exceptional circumstances" clause, covering areas such as injuries, suspensions and sudden retirements.
Ritchie said: "To be clear, this is still a restriction that says players who are playing overseas will not be selected unless in exceptional circumstances. That is the current arrangement and agreement.
"I've said before I think it's right, and I do agree with that policy. I do not think that was an impediment to the end result of what happened at the World Cup.
"The player situation is related to many things. How do you get access, a whole raft of things that is about partialities and sustain the English game. I don't think it is connected to the position of the coach.
"I've not excluded English coaches, I am merely saying we would look at international coaches as well.
"I think that is quite different to players. That is based on practicality of access and maintaining the strength of the English game. We want to see English players playing in England."
Woodward, though, has questioned moves to potentially recruit a foreign coach, while continuing not to look at individuals like Clermont Auvergne full-back and current European player of the year Nick Abendanon and Toulon flanker Steffon Armitage.
Writing in the Daily Mail, Woodward said: "At Wednesday's press conference, Ritchie confirmed he will lead the search for the next England coach, that the next England coach will report to him and that he will appoint someone with international coaching experience.
"I would love to know the specifics behind this. So we can't pick players who play abroad, but we can employ coaches who come from abroad? How ridiculous."
England's selection policy took effect after the 2011 World Cup, although it is currently a stance adopted by just two major nations - England and New Zealand.
Australia also operated with a similar selection outlook, but Cheika oversaw a change that now means overseas-based players with at least 60 caps and seven years' experience with an Australian Super Rugby team can be picked.
Toulon backs Matt Giteau and Drew Mitchell were among the Wallabies' star World Cup performers.