James Mortimer 16.Feb.2012Getty Images
Former Italy and Springboks coach Nick Mallet heads the contenders, and initially it was thought that the South African could team up with the Chiefs back's coach to form England's dream team.
Smith, who said last year he would be loathe to take his intellectual property overseas, is looking forward to working with the Chiefs and it was reported by the Telegraph that he may have been turned off by an extensive job description for the new England coach.
However he confirmed to stuff.co.nz that the timing was not right and was committed to the Chiefs.
"I understand they want to fill the position for the tour of South Africa in June. That timing doesn't fit in with me so I haven't put an application in," Smith said.
"I said I have a moral obligation to fulfil my time here with the Chiefs."
"I'm enjoying it (coaching the Chiefs). It's a bit of a step back in terms of pressure and it will be a good recovery period for me, I think."
Odgers Berndtson was recruited by the Rugby Football Union (RFU) to headhunt applicants, and it is believed that Mallet, along with former All Black John Kirwan and former Ireland coach Eddie O'Sullivan head the overseas candidates.
The only other high profile overseas coach who previously expressed interest was former Wallabies coach Eddie Jones - who recently took over from Kirwan as new Japanese boss.
Interim coach Stuart Lancaster heads the 'home grown' hopefuls, alongside Northampton's Jim Mallinder and London Irish's Toby Booth.
A five man panel will select the new coach with the criteria and details for the role said to be thorough and stringent after members of the RFU's corridors of power said that recent recruitment processes have been flawed.
Ian Ritchie, the new chief executive who takes office at the end of February, will oversee the new appointment.