Claims that a definitive shortlist with a quartet of names on has already been drawn up are wide of the mark, but as far as Tony is concerned, there is only one man for the job, and he says:
"It all seems easy for Trev at the moment, doesn't it?
"I think the main thing was that the club got a couple of good results while he was in charge, and hopefully it might have turned his head, he might say I fancy a bit of this' and stay on.
"But I don't think there is anyone I need to convince except Trev and maybe his missus!
"I'd like him to take it over and I think everyone would; it would give a lot of stability to the club.
"I don't know how he feels about it; he says he definitely didn't want it but he seems to be warming to the task, doesn't he?"
Tony knows it is important not to get too carried away by the two wins under his command last week and the unbeaten three games he presided over when he took temporary charge last season when Glenn Roeder was taken ill with a brain tumour.
"It isn't enough to qualify him taking over in temporary charge and he is not foolish enough to think that," he says.
"But if you know Trevor you know what high esteem he is held in the club and all over the country.
"So if he gets the coaching staff around him then I see no reason why Trevor couldn't take over the reins and make a big success of it.
"Everybody respects the man and if you don't respect a man like Trevor in football there is something wrong with you as a person."
As to the subject of the backroom staff, he adds:
"Trev might think that what he has got is enough with Paul Goddard and Roger Cross, but it wasn't enough last season so maybe they need to reinforce that staff if he is going to keep Sarge and Roger on, and I am sure they are doing a good job there.
"Maybe it could be someone with a bit of a firmer hand, a harder taskmaster, because, as Trevor has so often said there are a lot of personalities that you have to deal with at the club, even though we sold some strong ones.
"There are still some forceful personalities there and forceful personalities need a strong hand to look after them."
Again, he would like the West Ham tradition maintained and he adds:
"I think Stuart Pearce is fine but he had a year or so at the club and Alvin Martin has had 20 or so years at the club, Alan Devonshire had 12 years at the club, Ray Stewart had 10 or 12 years at the club - West Ham people, as far as I am concerned, and all of them strong people who were all part of a fairly successful side and know how to attain results."
Tony sees last week's two wins as being crucial to West Ham's chances of promotion, and adds:
"They have eased matters and taken a huge pressure off everyone - and a little bit of pressure off the new manager if Trevor decides not to take it because it gives him a little bit of a buffer, shall we say with 10 points on the board already.
"They were very important results."
In another way, though, Tony acknowledges there is pressure on the next incumbent as expectancy is high and the two back to back wins only serves to increase the pressure to carry on the good work.
"So it should do; although it is a thin squad, as everyone says, what squad in this division is a thick squad and what squad in this division is a better squad than ours?
"We obviously need to reinforce and the club has said it is looking to get two or three people in and if we do that I think we will be as strong as anyone," he concludes.