A particular concern is the midfield area - traditionally West Ham's strongest department - and he says: "We haven't got any cover - we have got four very good midfielders but after that we are relying on John Moncur, and I think he will be the first to admit at the age of 35 his role is probably from the subs' bench with one or two starting appearances.
"Laurent Courtois is a free transfer and Steve Lomas is out; it is a major concern for us because we have no strength in depth at all.
"We can put out a good team but the fact that the squad is very thin obviously makes life more difficult, because we all want to achieve this season.
"What will be crucial will be keeping players fit, but there are a lot of games in a short space of time, and that's where we need to be lucky."
But he is able to put the search for a striker on hold, and he explains: "I'd like to strengthen in two or three departments; I think we can safely say with the emergence of Jermain Defoe in the past month and Paul Kitson getting the hat trick at Charlton, that we have four strikers there who will be very dangerous on their day.
"But we are short in midfield and short for a couple of defenders of the quality you would want in the Premiership.
"I'm working hard in that department - we have scouts abroad and one scout travelling virtually to the other side of the world this weekend.
"Hopefully the reports will be favourable and we can do something about this particular player in the new year.
"We are not in a position to be buying any more players this season so we need to bring in a couple of loan players.
"We've had loans in the past that haven't been able to bring anything to the party, but we want ones that can go into the first team."
Despite links to several players this week including, most improbably, Brighton's Bobby Zamora, Glenn stresses: "There is nothing on the transfer front for this week and it is all speculation as far as I'm concerned; whether anything materialises next week I wouldn't like to say at the moment."
Reflecting on the win at Manchester United last weekend, Glenn says: "It was a great day for all of us, the whole club and all our supporters, but the next game comes round very quickly and it's equally as tough."
Of the tactical switch which saw him shuffle the midfielders around, he says: "I had thought about it leading up to the Manchester United game. I felt it would benefit us to mix our midfield players up and cause them a couple of problems, which is how it turned out.
"Don has scored 10 goals from the right for Sunderland last season; he is not an out and out winger, but he plays tucked in if you like.
"I think Joe will grow into the central midfield position as he gets older and stronger, breaking to the left and right; he has really good energy as he showed in the game, and Michael was excellent sitting deeper - and both are only 20 years old.
"Trevor was a real threat at Old Trafford, cutting in on his right foot, so I was pleased."
Glenn hails the win as even more pleasing than last year's in the FA Cup, and says: "People who saw us in the cup last season said we played on the back foot for virtually the whole game and scored on the breakaway, but it wasn't like that on Saturday.
"We had nearly as much possession as them and not many teams can say that - it was a terrific victory."
And Glenn doesn't want the fact that Manchester United rested certain players to detract from the victory, explaining: "I was quoted as saying I looked at the team sheet a couple of times but I look at every team sheet a couple of times whenever we have a game.
"I run through it once and again to be absolutely clear about the opposition's team and tactics - it is a normal thing to do.
"Solskjaer had scored in his previous six games against West Ham, Dwight Yorke is exceptional, Luke Chadwick will play for England one day and they don't come much better than Roy Keane, Nicky Butt, and Paul Scholes in the midfield."
Sir Alex Ferguson said after the game that West Ham dictated the early tempo, and Glenn says: "It was a great compliment and nice of him to say - but we have got to win that midfield again this weekend.
"Everyone knows about Vieira and Ljungberg, and Henry is the striker on form at the moment.
"Whether he puts Wiltord, Kanu, or Bergkamp alongside him, they are the most exciting team around but we are all looking forward to it."
Glenn welcomes Fredi Kanoute back with open arms and says: "In the 8 games he has played we have got 13 points which says an awful lot about the importance of Fredi Kanoute.
"A run of four games has moved Jermain on a notch or two but he is still learning the game; but the fact he got four games in augurs well for the future."
A win against Arsenal would be a nice belated birthday present for Glenn, who celebrated his 46th birthday on Thursday.
He says: "Any win is a nice birthday present; we are the same as lots of clubs trying to get the points we want as quickly as we can in what is a very tough league this year in terms of closeness.
"We are six points off the bottom three but two more points would take us to the top half of the table, and the annoying thing is we should have a lot more points and be sitting comfortably - but we are not.
"And we still have to play the top three in the Premiership in the next couple of weeks starting with Arsenal tomorrow, in what is arguably our toughest month on paper.
"I'm sure other clubs have their own hard luck stories but you only look at your own situation - we have thrown away winning opportunities at Charlton and Sunderland, and, on the second half performance, against Aston Villa.
"But you have to look forward and not look back, and an unbeaten run would do everyone the world of good.
"I am encouraged, but what we have to do is focus on the next game."
Meanwhile, Glenn says of Titi Camara, who made his first appearance of the season on Saturday: "Titi is finding it very hard to get back to the level of fitness that is required.
"Paul Kitson was not available to us at Manchester United and it was a straight choice between him and Todorov for the bench - and I went with Titi.
"But he is finding it difficult to get back to the level of general fitness that is required for the Premiership, and the motivation that is needed to get there.
"He has had a knee injury which he has recovered from and the coaches are working very hard with him - full credit to John McCarthy, who has been giving him a lot of personal attention."
Meanwhile, of the FA Cup draw that pairs the Hammers with Macclesfield away, he says: "You always want to be drawn at home but I have been reliably informed by Kevin Keen that it is the best surface in the division. That is important and I'm pleased that it is on TV, which always adds extra spice."
He rejects the notion that the cameras have chosen the game expecting an upset, and says: "The BBC are here for a game of football as far as I'm concerned; if anyone thinks any other way that is their perogative.
"We are doing the job properly. We will watch them at least three times and are treating them with all the respect they deserve."