Peter likes what he has seen from his short time at the club and he enthuses:
"He has done ever so well; there is no doubt about his quality because everyone tells you what a good signing he is - but now it is up to him prove it, because he has a point to prove to himself.
"I don't think he has got a point to prove to anyone else, because people will always question him and say rubbish like he is doing well only because it is the first division - but if he plays to his capabilities there is no doubt that we have signed a top quality player."
Another signing this week was that of Moses Ashikodi, a young forward with tremendous potential.
"He is only 17 but you try and improve your squads all the time whether it is at youth team level or whatever," says Peter.
"He played in the week, scoring two goals, and he gives you a rawness; yes, there are a lot of improvements still to be made in his game and he is a while away from the first team, but if he gets coached well and listens to the advice he gets to make him a better player he has an opportunity in the game.
"There are not many people get the opportunity to play for West Ham United so this is a great chance for him - and hopefully he can take it."
Peter says West Ham will be able to cope if Michael Carrick moves on, adding:
"It always happens with good players, and the biggest disappointment you get is when nobody is interested in your players - because that means you don't have the quality that other people want.
"The only problem is probably the timing of it; you would have liked it to happen earlier, so that you would be prepared going in to the first match.
"Obviously he is one of our top players and all of a sudden, a day before the season starts, he could end up being taken away - but that is football, and that is one of the fallouts you get from the disappointments of last season.
"All the best players want to play in the top division and there is no fault on Michael there at all; the top scouts should be interested in Michael Carrick because he is quality."
He says that if Michael does leave, it will be up to another person to take responsibility, and explains:
"You are hoping that everyone else can play well; too often last season we didn't have enough players playing well at the same time and everyone seemed to lose a bit of form at the same time, unfortunately.
"We are looking for more from them and we are hoping that with the quality we have got in the squad we can play better and more consistently.
"We have added quality with Rebrov, Sheringham and Chadwick, and on paper we look a very good outfit but it is not won on paper - it is what you do on the pitch that is going to count."
Peter can't wait for the season in earnest to begin, and he adds:
"I wouldn't say it just anticipation, it is excitement because we are all looking forward to a new season; football is all about twists and turn.
"The excitement the fans get is no different from that the players and the coaches and the managers get at this time.
"But sometimes there are concerns - and you are hoping all the hard work you have done in preseason comes to fruition.
"Now it is down to the serious stuff which is obviously getting points on the board again - and that is what we are desperate to do."
Looking back on the 4-4 draw with Anderlecht, he says:
"It was a game for getting fit because the biggest goal was getting as full a squad as we could to choose from; we only have Steve Lomas and Don Hutchison injured from the first team squad.
"Now we are going into this game with everyone else fighting fit and raring to go and everyone starts the race together - I just hope that in May we are at the head of it.
"Anderlecht gave us a few pointers about the things we don't want to happen in the season, and hopefully we have got those things out of the road in the friendlies, where you make mistakes and don't get punished.
"In the league you get punished big time for mistakes - and hopefully we don't make too many of them."
Speaking ahead of the trip to Leicester, he adds:
"Leicester are the big favourites and have added 10 or 12 players; looking at their squad it is probably as good as any in the division.
"It will be a full house in a big stadium - and a fantastic way to start the season with expectation on both teams.
"They will definitely be there at the end of the season, there is no doubt about that, and if we get the three points it will be a fantastic start to the season."
Peter will see David Connolly for the first time since his departure in the summer, and he adds:
"David was excellent for us and it is a disappointment to see players of that quality go; but that is part and parcel of football and if you don't get back into the Premiership you can't afford to hold on to all the quality players you would like.
"If people show an interest sometimes you have to accept it - life goes on.
"David will be desperate to do well, not just because it is West Ham he is playing against but because that is the type of character he is.
"He wants to do well in every game and I hope he does that for Leicester - but not on Saturday."