Brighton manager Gus Poyet has ruled himself out of the West Ham job as club co-owner David Sullivan vows to get the right man to resurrect the Upton Park club.
The Hammers have vowed to have their new boss appointed by the end of the month as they look to bounce back from the npower Championship at the first attempt.
The Irons' finally wielded the axe on Avram Grant - only appointed during the summer - after relegation from the Barclays Premier League was confirmed on Sunday after they squandered a 2-0 lead at fellow strugglers Wigan to lose 3-2.
Former England manager Steve McClaren has already ruled himself out of the running, with Martin O'Neill reported to be head of the wanted list again, the board having offered the Northern Irishman the job during January only to be turned down.
Poyet had been linked with the vacancy after steering the Seagulls to the League One title but has ruled himself out of the running.
The 43-year-old Uruguayan told Sky Sports News: "No chance. I can promise I will never apply for a job during my time at another club, especially at a club like Brighton where I'm so happy to be.
"It would be really silly on my part to apply for any other job. I promise you at the moment there is nothing, just rumours."
Sullivan admitted the appointment of former Chelsea and Portsmouth manager Grant following the dismissal of Gianfranco Zola was a "bad selection" by the board - and it is not a mistake they intend to make again as the east London club face up to life back outside the elite clubs of English football.
"We will wait to see who applies and wait to see what happens generally, but it will be resolved within two weeks, I should think," Sullivan said.
"I think we will definitely get an English manager, or a British manager.
"We do need someone who understands the culture and if you get someone with a knowledge of the East End that's so much better."
Sam Allardyce, sacked by Blackburn in December, has also been linked with the vacancy, along with former Chelsea midfielder Roberto di Matteo, the ex-West Brom manager, would both appear to have been ruled out by Sullivan's comments over the need for a home-grown boss.
Chris Hughton - who guided Newcastle straight back up and to mid-table in the Barclays Premier League before his untimely axe at St James Park earlier this season - and Watford boss Malky Mackay are both former West Ham players, so are expected to be in the frame,
Neil Warnock and Paul Lambert already have top-flight football ahead with Queen's Park Rangers and Norwich next season, so it is unlikely either would jump at the chance to oversee one more campaign battling to get out of the Championship - and at a club burden by a multi-million pound debt.
Paulo di Canio achieved cult status during a four-year spell with the Irons from 1999 to 2003 and has a lounge named after him at Upton Park.
The Italian's appointment would certainly be a popular move with supporters.
However, Sullivan insists emotions cannot play any part in what is likely to be the club's most important managerial decision for a decade.
"The problem with Paolo is, although the fans would love it, I am being realistic and he has no experience whatsoever being a manager," Sullivan added.
"If you look at first-season managers the failure rate is enormous.
"If he had done a season anywhere and was, say, top of Serie B in Italy with a team, I would take the chance.
"My heart would say Paolo and the fans would say Paolo - but with someone who is a complete novice as a manager, with no experience, you just can't go with it."
West Ham are already burdened by massive debts, so the loss of much-needed television revenue is set to hit hard.
Sullivan, though, maintains he and co-owner David Gold, both life-long fans, will inject more cash to keep the club afloat as they look to get back into the Premier League at the first time of asking.
There will, however, be no escaping a fire-sale at Upton Park, with England internationals Robert Green, Matthew Upson, Carlton Cole and Scott Parker, the FWA Footballer of the Year, all set to leave.