West Ham co-owner David Gold says the club hope to move quickly to find a replacement for Avram Grant, but their overriding concern is to make the right appointment following the club's relegation at the weekend.
Grant was relieved of his duties on Sunday after West Ham let a 2-0 lead slip to lose 3-2 at Wigan, confirming the club will compete in the Championship next season after a long and difficult campaign in the top flight.
Former England manager Steve McClaren is already odds-on favourite to take the job at Upton Park, but Gold says the West Ham board will not be rushed into an appointment, even if time is of the essence.
"The sooner the better," Gold told Sky Sports News. "That is important. The sooner the better because there is lots of work to do, an enormous amount of work, but at the same time we mustn't be rushed.
"This will be a very, very important appointment. You are choosing a manager that is good enough to get you out of this division, which is the Championship, and capable of continuing once we have achieved that.
"We are looking at everybody. More importantly, now it is known that we are looking for a new manager and this is one of the reasons we moved quickly, it is one of many reasons of course. It is important we have time for CVs to come in to us.
"I am sure there will be many, many managers who see the West Ham job as challenging, exciting. Not only will we be fighting to get back to the Premier League, but we are also preparing ourselves for probably the most exciting event in the history of West Ham Football Club in the sense that we will be moving to a new stadium, which is something we have never done.
"All of these challenges have got to be addressed, and it is important that we pick the right person."
In May 2010, and prior to Grant's arrival, Gold and Sullivan also published a ten-point manifesto for the club, the first of which was to "appoint the right manager".
Meanwhile, players such as Scott Parker and Thomas Hitzlsperger are now likely to depart Upton Park, with Gold conceding that if asking prices are met, then the club's stars will be removed from the wage bill over the summer.
He said: "We are going to do everything in our power to keep our best players. It is very, very difficult, as I have said in the past, it will be very difficult to ask an international to come and play in the Championship when traditionally England players aren't picked from the Championship ... by the same token I would hasten to add that we are not in any hurry.
"We must receive the proper amount of compensation for any player that we sell. And if we don't then that player will stay with us in the Championship."
When pressed directly on the future of Parker, who secured a place in England's starting XI this season and was named Footballer of the Year, Gold said: "I really have no idea. I am still just recovering from the pain of relegation and I really have not gone that far. Obviously one of the most important things will be bringing in a new manager. That will be our key requirement."