Sir Graham Henry and Warren Gatland have already ruled themselves out of taking over as England rugby coach.
Stuart Lancaster paid the price for host nation England's World Cup failure when he resigned as head coach overnight following a Rugby Football Union (RFU) review.
An RFU statement said Lancaster, in charge since April 2012 and under contract until 2020, had "stepped down by mutual consent".
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Jake White, who coached South Africa to World Cup glory in 2007, and Australian Eddie Jones are among the leading contenders to replace Lancaster, along with English coaches Rob Baxter and Mike Ford.
Australia's Michael Cheika, All Blacks assistant Wayne Smith and Sir Clive Woodward have also been mentioned but former British and Irish Lions halfback Dewi Morris wrote on Sky Sports that England should chase Henry.