Some sections of the media have been speculating about who might move on in the summer and, equally prematurely, two newspapers have 'exclusively' claimed West Ham's wage bill has to be trimmed by 30% this summer come what may.
This has been dismissed by the club, as has the claim that Fredi Kanoute wants to move on at the end of the campaign - lies which Fredi admits have hurt him.
Such notions aren't entering Trevor's head either, and he says: "Until it is mathematically impossible I am definitely feeling that we are going to be in the Premiership next year.
"There is going to be another team dragged into it, I have a funny feeling about that. I won't say who it is because that starts all kind of speculation but I think we are going to be in the Premiership next year and I am determined to put every effort in to make that possible.
"Obviously it is not ideal but I am part of the reason why we are not where we consider we should be and I am trying to get on top of my game and improve on it week in, week out, to put West Ham in a more desirable position - and I am happy about doing that."
As for thoughts on what might happen in a worst case scenario, Trevor says: "Hopefully it is not going to come down to that anyway, because we are going to be in the Premiership next year and there won't be any questions asked.
"People will hopefully be looking back thinking 'we got last year's terrible start and mid-season out of the way and managed to stay in the Premiership, now let's look forward to next year.'
"We want to prove that when we finished seventh it wasn't a fluke and we want to reproduce what we did that year.
"There is no point in talking about it yet, we just have to make sure we maintain our Premiership status this year."
And that desire to not only stay up but then excel next season is certainly part of Trevor's thinking.
He admits: "I don't really want to speak about it but I am sure this team that we have got here can reproduce what we showed last year - let's hope we all get the opportunity to do so, and let's all battle to make sure that we definitely do.
"Everyone knows what is at stake and what is needed. We are all going about our jobs in the best way we possibly can and let's hope we get our just rewards."
The reward he speaks about is obvious enough, but as a little fillip towards that aim Glenn Roeder received the Manager of the Month award last week to recognise the team's recent achievements.
All of which leaves Trevor blissfully unaware and he smiles: "I didn't even know he got Manager of the Month - that shows you how much telly I watch, which is what two small children do to you!
"I am pleased for Glenn. It has been a tough season for him and he has had to take a lot of critics having a go at him saying he is not good enough and all that.
"I think there is a jinx when someone gets Manager of the Month so let's hope we can break that record as well as breaking the record of being the first club to stay up after being bottom at Christmas."
Trevor is hoping to reverse the 4-1 defeat at Villa Park earlier in the season, and he adds: "I don't believe they stuffed us but it was a terrible result; we were well in the game and then all of a sudden they took over late on and we got caught cold.
"It was when we were on a really bad run and we added to their strengths by not performing as well as we know we can - and not battling as hard as we are doing now.
"So it is going to be a completely different game and I am sure they will echo that after the game, whatever the result is."
While fans' nerves may be shredded, Trevor insists the players are keeping calm under pressure, and he stresses: "Every game is as important as this weekend's game and unless you have seen something that I haven't seen the lads have dealt with it fantastically.
"One of the reasons we have done that is that we have been down there or thereabouts nearly all season and just because it is the last few games it isn't making the lads tense in any way.
"We are just playing our football in the way we know we can, picking up the results, and I don't think we are going to be going in to the game with any nerves at all.
"There is belief and determination - those two words stick out for me as the most important things about our game - but nerves are definitely nothing to do with what I am thinking."
As for the overall battle, he says: "I think it is looking like a real massive mountain to climb for the two bottom clubs, but then there is ourselves, Bolton, Fulham have a tough run-in, Birmingham are down there, Villa are not too far in front, so there are a few clubs in there that are going to be dragged back into it.
"I just have a feeling that us and another club are going to be able to steer clear of the drop.
"I am feeling great and really looking forward to the game."
Looking back on Saturday, he adds: "It was a tough day to play football; it was roasting hot and to be honest Southampton came out of the blocks on fire to put us under a lot of early pressure.
"We dealt with that until the final minute of the half which was a disappointing time to let the goal in.
"I thought it was a good goal myself, a controlled finish, because he tried to keep his eye on the ball, get his foot over it, and just direct it in - and if you do that you have always got a chance of scoring from so close.
"The lads worked hard in the second half and I think we thoroughly deserved what we got out of the game. The longer it went on I thought the more likely we were to score.
"I had a chance but unfortunately it was on my left foot. I tried to get over it as much as I could and hit the target, but he saw it all the way which made it a lot easier, and in the end it was quite a comfortable save.
"We had quite a few chances in the second half, and it ended up being Jermain Defoe again who got us the point that we thoroughly deserved."
Trevor is due a goal to add to his brace at West Brom which started the revival and he adds: "I am getting into positions which is all I am worried about. I feel I am working hard and making sure I am giving all I can to the team for the best opportunity for us to get the points that we need."