"I think most of the players want him to be manager and everyone respects him - his training is good and he just knows what he is on about," says Matthew, who was given his debut to at left-back on Saturday against Ipswich.
"Nothing has been said, and it is hard, but I think he will take the job - hopefully he will, anyway - and if he does I can see West Ham going straight back up.
"He has so much experience in the game and when he says something you know it is going to be right.
"Everyone listens to him first time, and if he says it, it is done - whereas some managers need to tell you more than once."
Matthew, normally a centre half, made his debut at left back at Portman Road and says: "I loved every minute of it; I played at left back, which is not my normal position, but I enjoyed it.
"I did play there when I was under 17, just the once, and it was a bit funny at first but once I got into it it was fine.
"I was worried because I didn't want to mess up or anything, but I got my first touch away and played it nice and easy.
"Christian, Tomas, Ian, and Jamo at the back definitely helped me through it and were all very good.
"It was a chance for me to get in the team and I was very happy to get that chance so I wasn't going to turn it down.
"Trevor just said 'we haven't got a left-back so how would you feel about playing there?' and I said 'definitely' - we just took it from there, really.
"He said to me he thought I could do the job because we tried it in training the day before.
"It is very different because sometimes you are looking over your shoulder and only the crowd is there, not your other centre back - it is a bit wierder.
"But you get a lot more of the ball bombing up and down the line and getting the crosses in.
"Matthew Etherington was helping me out, giving me some nice angles, and helping me in defence as well.
"I was happy to play and I have found that the West Ham fans are brilliant; it was packed where they were and they helped me through it.
"I just want to get the experience of playing against better players in front of big crowds and hopefully, if I go back after these three months to Leeds, we can see what happens."
Whether West Ham bring in a left back - manager or not - before the Reading game remains to be seen, but if not it may be that he will continue in the role.
"There is no game this weekend but we will keep training every day," says Matthew, who actually made his Premiership debut against West Ham for Leeds last season - where one of his first tasks after coming on as substitute was to mark David James coming up from a corner.
He admits the second half on Saturday became a bit fraught and adds: "They were putting a lot of pressure on the ball in the second half; we scored straight away after half time and when you get 2-0 up you just change your game and start defending for some reason.
"They got a lucky goal with a deflection and that can change a game but Jamo made some good save as well.
"You don't want to make a mistake or he will be right on you but he talks you through it as well - he is very good communicator."
One thing Matthew does hope about the new manager is that he at least recognises him - unlike several autograph hunters at Ipswich at the weekend.
He reveals: "I got a couple of Carrick shouts; one kid had me signing pictures of Carrick but I told him afterwards I had ruined his picture - but I haven't told Michael!"