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.
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"I am wholly committed to the Stormers.
"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 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.
