Fredi is a serious doubt for the trip to Leicester on Saturday and Glenn says: "He was running on Thursday morning and I have not ruled him out yet.
"What we're worried about now is if Fredi Kanoute is going to be out for any length of time, because you could quite easily see in the opening 45 minutes of the Arsenal game how crucial he is to us.
"There is nothing else like him at the club, and quite honestly I don't think there is anything too much like him in the Premiership full stop. He has improved so much this year.
"He has missed half the season already with only nine starts, but in those nine starts he has scored six goals.
"But it is not just the goals that have impressed me, it is his general performance in those games and the problems he has caused the opposition when he has played.
"He is improving all the time and if we can only keep him fit and well and playing as many games as possible in the second half of the season, I'm sure his performances will force an opportunity to get into the French senior squad.
"I think after the obvious French strikers - and they have the luxury of some wonderful strikers in Henry, Trezeguet, and Wiltord - there is a group of younger strikers like Kanoute, Cisse at Auxerre, and others that I think would hope to get a run out in a friendly before France choose their World Cup squad.
"If Fredi stays fit he can do it. He is priceless to West Ham, he has proved that this year and what is critical is to keep him fit.
"When he has been, he has been out on the training ground every day which at times hasn't always been possible since he joined us."
Glenn thinks the best is yet to come and adds: "He has got such a big frame, and he is still a young man strengthening up, so if we can get some more strength into him it will be good because he has nowhere near reached his limits and I don't think he will do that until he is 25 or 26.
"He is already some player and at 25 or 26 he is going to be exceptional but all I am worried about at the moment is having him fit for the next 20 games or so."
Glenn admits that no transfers are imminent despite the fact that he thinks the squad is too small, and he adds: "There is nothing to report in the transfer market at the moment. We're looking, without doubt, and I hope I'm not put in a position where I have to bring a player in that I don't have full confidence in to play Premiership football.
"You can never say never in this game and if we were to have a run of injuries that we couldn't afford I'd have to press the panic button. There is always a list of players out there that are okay but not really what you are looking for, but I don't want to have to go down that route, and that is where you need to be fortunate."
The 'engine room' concerns him particularly, and he says: "We have got an excellent midfield at the moment though we are very light on cover, but in the last two games we have had an exciting, hard working midfield.
"I could do with John Moncur being fit and well during the Christmas games which start on Saturday and we need Steve Lomas when he comes back at the end of January as well."
He feels the Hammers are due a bit of luck and explains: "Just of late the boys have played some very good football but we haven't always got our just rewards, I have to say that.
"We certainly didn't up at Sunderland and the battering we gave Aston Villa in the second half deserved a point and could have warranted all three, but it wasn't to be.
"I really feel the 20 points we have picked up this season have been hard earned and fully deserved."
David James missed Thursday's training session with a heavy cold but will definitely be training on Friday.