The new man will become only the club's 10th manager, though, as an illustration of how the game is changing perhaps, the fifth since John Lyall left in 1989.
Indeed, before his appointment in 1974, West Ham had had just four managers - Syd King, Charlie Paynter, Ted Fenton, and Ron Greenwood - representing an average length of service of eighteen and a half years.
Since John's departure, however, Lou Macari, Billy Bonds, Harry Redknapp and Glenn Roeder have averaged just over three years at the helm.
That statistic, though, is affected to a large degree by Lou Macari staying less than a season before he resigned after taking over in 1989.
As an "outsider" his arrival broke with tradition, whereas his sucessor Billy Bonds, and then Harry Redknapp, had both played for the club.
Although Glenn hadn't, to his regret, ever done so, he was a West Ham fan and was of course promoted from coach at Upton Park.
So whether the next manager has any previous connections with West Ham is a question on everyone's lips - can Trevor provide a clue?
"I have got an open mind personally but it does help because you only have to look at past history to see there have been some good examples.
"And even with my brief flurry myself, the crowd have been fantastic to me because they know I have got that affinity as a player, a fan, and a director.
"There is that patience and whatever to support you and it is a plus; if the person happens to have that background it will probably give them more time to get things right.
"But then again if the person gets the winning formula players fans wouldn't care where he came from.
"It is an appointment that is virtually impossible to get the unanimous view that everyone will say 'that is the right one'.
"We have got to get the balance; we want to get it right but we don't want it to drag on.
"We would like to feel that when we get someone there will be a period of stability and they will get the opportunity to do what is needed."
But would he reconsider looking to take the post?
"To be honest, I have not looked beyond the Ipswich game; we will get that out of the way and then I will need to sit down and see how we are getting on with the process of elimination.
"Then towards the end of the week I am off to Macedonia with the BBC anyway, and a lot of the lads will be away as well so nothing much will be happening.
"It is a case then of seeing what progresses; I have said I will try and continue in the role until we all feel we are going to make the right appointment."
Speaking ahead of the trip to Ipswich, who have drawn 1-1 against Reading and Coventry and lost 1-0 at Crewe and Wigan, he says:
"I am a bit surprised they have had two draws and two defeats; I would have expected them to be in the top six battling it out.
"So for them they have not made the start Joe Royle would have liked and I can assure the team that he will be up for the game against us because he will look on it as a way to get the crowd going and perhaps kick start the season.
"Having said that, when you haven't got a win the confidence must be a little fragile so we have got to go there on the back of our performance and put them under pressure.
"We have all been in a situation where we are a bit edgy and looking for the win; what we want to make sure is that one of those potential rivals later in the season doesn't win to be two points behind us but that we actually beat them to go eight points clear of them.
"The squad has got few options as such, and that is not being unkind to the lads here because the spirit is good and they are working hard to try and get the results.
"But we need a minimum of three extra players irrespective of injuries with Rob Lee out but coming back quicker and Steve Lomas out at least for a couple of months and Rufus out for a further three at least.
"Without them we are certainly three short, I would have thought."