The England international put in a transfer request earlier in the season which he subsequently withdrew, but recent reports have implied he was unsettled because of a hankering to play European football.
But he reveals that he is so impressed with the way things are working out under Glenn Roeder that he wants to extend his stay.
He reveals: "Basically I have been in negotiations with West Ham, looking at my situation, and hopefully we can come to some agreement between now and the end of the season - or through the summer - that will suit all parties.
"That would mean me staying at the club and happy with the club's ambitions, and hopefully we can sort out signing a new contract in the next few weeks.
"I'm very happy with what Glenn has done. He has come in and he has steadied the ship, he is a pleasure to work with, and everyone gets on well with him."
With the Hammers moving up a gear at just the right time, he adds: "We need to keep the momentum going, and if we do finish seventh, it will be a great achievement after what we have been through and the start we had.
"If you look at the table it will be like finishing top of that second league within the Premiership - and that is a good start to Glenn's managerial career in the top flight.
"If he is given the finances and the support I'm sure he can take the club to the next level.
"Then you are looking to break into that top seven. There is a big gap at the moment, but if he is given the right finances I'm sure he can take West Ham into that top group."
Trevor, in Cheshire preparing for England's friendly with Paraguay on Wednesday, has no idea whether the injury to David Beckham will work to his advantage.
When asked whether his possible absence from World Cup games would enhance his own cause, he says: "I don't know. It depends what is in the gaffer's mind because if he feels he wants to play me on the left it doesn't probably affect my position whether I am going to be in the squad or not.
"Obviously if he is thinking about playing me on the right as well it might have some bearing on it, but you never know.
"It is difficult for any player who is on top of his form not to be able to go to the competition so hopefully he will be able to get himself fit."
Trevor is delighted with getting a point at White Hart Lane on Saturday - not least because of where he lives, on the Essex/Hertfordshire borders.
"There was a lot of hard work from the lads and I think after the game we felt we thoroughly deserved to come away with something," he says.
"With the chances we created it would have been harsh not to get anything, and it would have been hard if we had lost, especially as we all live in an area where there a lot of Spurs fans as well as West Ham ones.
"There are a few people that you bump into day by day who are Spurs fans, so I'm glad we made sure we got a result on Saturday - Pearcey has saved us a bit of grief!"
He says the point went some way towards atoning for the home defeat to Spurs earlier in the season, and adds: "We got thoroughly beaten at Upton Park. They were on top of their game and they really did give us a good hiding even though it was only 1-0.
"So we went into the game with a lot more determination after what they did to us."
And Trevor says he was envious of Ian Pearce scoring such a spectacular goal.
"I would have been very proud of that. It was an unbelievable strike and everyone is happy for Pearcey because it has been a hard time for him coming back from his knee injury," he says.
"As everyone can see he is becoming a vital part of the squad again. He is well liked by all the players, he gets on with everyone, and he is coming back from a career threatening injury which shows a lot of character, and he is a top bloke.
"We are all really pleased for him, and you could see that at the final whistle when everyone went up to him - he saved us from defeat against our arch rivals."