Lee has signed until the end of the season, but there has already been a clamour amongst delighted fans seeing 'one of their own' at the club for him to stay beyond that.
But Trevor says: "I think it is too early for everyone, and there are too many imponderables, but it is a five month period which will benefit everyone. If we retain our Premiership status that hopefully will mean the side has done okay and Lee will have contributed.
"It is a chance for him to get to know the players, if we have survived then you can look at that - and hopefully the impression from both points of view will be favourable and you can kick it on from there.
"That is an option I think everyone hopes develops but it is premature to start talking like that because everyone knows there are too many 'ifs' at the moment.
"It is definitely not ruled out, though, at the end of his stay he will be a free agent in the summer - and we are all conscious of that.
"Initially, we are all hoping the short term works out for everyone, and if it does that will put him in a stronger position, but it will have given him some time at the club and he might have got an affinity with it from a playing point of view.
"It would be wrong for us to say 'we definitely know we can keep him' because we know that is not the situation - and I am sure he wouldn't want to convey that.
"But you hope the four or five months goes well enough that everyone emerges positively from all the queries at the moment, and we are at least in a position to talk about him.
"If it goes very well, it could make it more difficult to retain him because he will have showed his worth, but you then hope the four or five months will have been enjoyable for him and give us that starting point on ongoing discussions.
"We just have to help him get back to the kind of football he is capable of in some of the exciting games ahead.
"He has got Arsenal, Manchester United, and Liverpool all in the first month - and that is better than sitting around.
"That is the option that some players would have taken but I just think this is the right decision for him after some of the negatives of the last year or two."
Lee is a confirmed admirer of Billy Bonds, and Trevor says: "It doesn't surprise me. People have been joking to me to get my boots out but I have said to them the one player we need at the moment is a young Billy Bonds to fire up the team in the right way - and really drive the team on.
"I think Bill was a wonderful inspiration to everyone. Lee is a different type of player, but I think he will be a driving force and it will rub off on some of the other players."
Trevor reveals that discussions had been taking place for some time to bring Lee in and he says: "It had been bubbling on for quite a while and one or two other clubs were mentioned.
"But it was a unique situation - a player who last year was worth £10m or £15m becoming available initially to the end of the season.
"From a playing ability point of view I don't think anyone has any doubts that it will help him get back to his best form and help the side.
"Obviously there is the discipline and the problems he has had away from the pitch which naturally get some of the media focus but, from his point of view, coming back to London is probably ideal for him.
"And it is an opportunity for him and ourselves to try and make sure we retain Premiership status - and see how it evolves from there.
"There have been comparisons with the Paolo signing after the problems he had - and that gamble has been hugely successful.
"They are different types of individuals and there are different reasons for how the possibility has arisen.
"But, if you look at it from Lee's point of view, he has to re-establish his career and he should be getting towards his peak.
"For different reasons he has had a difficult 18 months and I am sure he would just like to get back playing football - hopefully West Ham will give him the stage to do so and get the rightful headlines."
Discussing his strengths, Trevor adds: "I think that any club coming up against him in the last few years would be conscious he was a player that could cause you problems.
"He has got the ability to score goals from midfield and he can give us that width and aggression, when it is channelled in the right way, so there are lots of pluses.
"Even when he was playing for Leeds this season he wasn't playing his best and with his contract there finishing this summer it was probably better for all concerned that he went now.
"It was an opportunity West Ham needed to take once it was there - and from the point of view of his playing you can't question it.
"The reality of the situation is that the opportunity would not have been there if there were not problems off the pitch, as such.
"From the fact that he has been about a year from playing his best form Lee will hopefully look on it as the chance to play the way he can in a West Ham side that, despite where we are in the league, is trying to play the right kind of football.
"I think he will enjoy his game and it will give him a platform where he can get back to his best form and everyone can benefit.
"I don't think myself or Glenn or anyone needed to be convinced from a footballing point of view that it was an opportunity that had to be taken."
Indeed, Trevor hopes the signing will just be the start of an upsurge in fortunes for the club and he adds:
"Getting him and one other striker, and getting Paolo and Fredi back by the end of the month, suddenly you have something that Glenn hasn't had all season, and that is competition for places.
"At the moment he can't leave people out who perhaps should be left out because you haven't really got the quality to bring in.
"Hopefully that will change in the next three weeks."
Looking at the battle ahead, he adds: "It is no secret that it is going to be a dogfight; there are four definite sides in it and it is quite amazing there are only four points separating them.
"The other three sides are probably looking on it as fortunate as we are that you are only three points away from getting out of the bottom three.
"But then there is a little gap and possibly, realistically, only Fulham and Birmingham are likely to get dragged back into it - unless someone has a torrid latter part of the season.
"The important factor is to get a bit of confidence back into the team after going through the holiday period following a disappointing couple of home draws.
"But it was a good display against Blackburn and a nail biter against Forest to get us through the psychological home barrier.
"Nobody is under any illusion, with eight home games left, that that is the key because the away form is not bad.
"But unless you can win four, probably five, of those home games between now and the end of the season, we are going to be in trouble."
As for the opposition for Lee's possible debut, he concludes:
"I have seen Newcastle a couple of times recently and they are very exciting going forward.
"Naturally we will benefit from Shearer's absence though Ameobi is a good player. Bellamy is probably the key man with terrific pace and acceleration and we are not strong sometimes at dealing with that.
"But at the back they are vulnerable as Wolves showed so it is a case of trying to get at them at every opportunity while realising we are dealing with an exciting side, particularly if Dyer comes back into midfield.
"They have a lot of good options in that area and the only thing I will predict is that it probably won't be 0-0."