With Paolo Di Canio and Tomas Repka suspended tomorrow, Sebastien Schemmel and Trevor Sinclair missing the Middlesbrough game on February 23, and Christian Dailly and Nigel Winterburn just one booking away from a ban, the defence, especially, will endure some reshuffling in the weeks to come.
In addition, Michael Carrick is out for five weeks after a groin operation.
It means the squad's reserves will be stretched in the coming weeks and Glenn says: "We are all looking forward to the rest of the season, but as I have said before, it is so important we don't pick up many suspensions and injuries.
"Over the next few weeks that is obviously going to be a big concern for me. We have lost Michael for the next few weeks and we don't want to have a run of further injuries.
"It is covering old ground, but we don't have any strength in depth. We don't double up in enough positions."
Of the 38 numbered players at Upton Park - of whom six are goalkeepers - 18 have made less than 10 starts for the club.
Of those, six have never played at all and four have only appeared as a substitute.
Included in the 18 are Gary Charles and Titi Camara, who have been beset by injuries and cost around £3m between them in transfer fees alone - they have unfortunately only made seven starts between them.
Of the 20 who have made more than 10 starts, six have their contracts up this summer and one is currently out on loan.
"It is a problem that has been with us from the first game at Anfield all the way through," says Glenn.
"With the medical team, the fitness coach, and the way we train them, we have survived with a very small squad, but we have to make sure over these next 13 games that we keep everyone fit to allow us the best opportunity to have a good finish to the season."
Glenn has been working on lifting the mood after the FA Cup defeat against Chelsea on Wednesday, and says: "We started on Wednesday night and we had a constructive chat about sowing the seeds of getting on with the season and not feeling sorry for ourselves, but getting as many points as we can as soon as we can.
"The players came in for a warm down on Thursday, and one or two had bumps and bruises, so we will assess everything ahead of the game.
"Obviously we have got a few problems with Tomas suspended though we expect Fredi to be fit. We are having a count-up to make plans for the trip.
"Paul Kitson worked very hard on Wednesday and Jermain had an excellent evening, but it goes without saying that having players of the calibre of Paolo, Fredi, and Michael Carrick missing is going to make it that bit more difficult."
Now, says Glenn, is the time to get a creditable result on the road, and he adds: "We need to have a good result away from home where we haven't done at all well. It is vitally important with Bolton below us that we come away with a good result."
He identifies Michael Ricketts as the danger man, and says: "He is having an excellent season and is improving all the time. He is going to be a force in the Premiership in the next few seasons and he is one we are going to have to keep an eye on."
Hayden Foxe is expected to deputise for Tomas Repka, but whoever comes in will have to show they are worthy of first team football in the future, says Glenn.
"It is an opportunity for someone else and it is important that, whoever that is, they take it," he insists.
"We have got to kick on now and concentrate fully on the league to see how high up the table we can finish.
Meanwhile, Glenn is rueing the decision of Robert Lee to go to Derby County this week, and admits: "He was certainly one we'd have liked to have brought to the club but it hasn't happened and we'd like to wish him all the best now."