Talking of some of the speculation concerning Lee's deal, he is keen to put the record straight.
"I have been told, though I haven't seen it, that there are some wild and ridiculous figures being bandied about concerning what Lee is reputed to be earning and what bonuses he might be getting for us staying up," he says.
"I can tell you now that Lee Bowyer has fallen into our pay structure; he wasn't difficult to deal with, and Paul Aldridge didn't take very long to knock out an agreement with his agent."
One of the wilder claims being made [apart from the one that Paolo Di Canio, who is actually in Bologna, shook Lee's hand on his first day] is that Leeds tried to negotiate a 'leave of absence' for him in the forthcoming visit to Elland Road, but Glenn adds:
"A contract is very private and personal and I wouldn't discuss anyone's - it is completely confidential.
"But it is important that people know that he wanted to come and play for West Ham, and when I spoke to Lee all we discussed was the football side.
"An agreement with Paul was arrived at quickly and Lee has not gone outside of our pay structure at all."
His initial day of training went well, and Glenn adds:
"It was a very snowy Chadwell Heath for his first day, but I am glad we can get on with him starting his career with us, hopefully on Saturday.
"As everyone knows he has had a few weeks out now, but he had two or three days running in Leeds, trained very well today, and has created a buzz around the place with the other lads.
"We have been in the 60 by 40 new sports hall; thankfully we have got that now, otherwise we would have had nowhere to train this week.
"What with the win last weekend and Lee signing there is a really good atmosphere, and I have to say he showed an awful lot of quality in the training session.
"He got a great reception from the players today; they all wanted to have a chat with him, be involved with him whether in the dressing room before training or at lunch afterwards, and it was a fantastic response from the players - it certainly gave them a lift having him around.
One of those players, captain Joe Cole, says:
"What is important about Lee's arrival is that it means there is extra competition for places, and that will keep everyone on their toes, but it is unfair to put all the pressure on Lee alone because it's up to every single player to do his best to get us out of this situation we are in.
"But saying that, Lee is a fantastic player and it's great to have him at West Ham - it's a brilliant signing which has given everyone a massive lift."
As for Lee's chances of playing for the full game at the weekend, Glenn adds:
"We will just have to see on Friday what part he can play in the game against Newcastle; he has been out for three or four weeks and his achilles has cleared up now, thankfully.
"What is also good for us is that he is naturally fit and he doesn't take a lot of getting ready.
"We will have a look at him in training on Friday and decide whether he can start or not, but I am hoping that he can.
"It would be a real boost for him and everyone and it goes without saying he would certainly prefer to start - and if he can, he will do.
"He is here to play but I wouldn't play him at the risk of breaking him down.
"But from what I saw in training this morning it certainly gives me a lot of encouragement about him being able to start."
Glenn is still having to face the - good-natured, but begrudging - wrath of rival managers at Lee's capture and he reveals:
"I have spoken to three Premiership managers in the last couple of days who all wanted to sign him; I have been told there were another three or four who would also have liked his signature, so we have done ever so well to convince Lee to come to us."
One manager not moaning, though, is Terry Venables, whose reaction to Lee's departure was the philosophical observation that, as a union man, he believes all players should be allowed to leave at the end of their contracts, however disappointing that might be for the club concerned.
That Lee's contract was not quite up in Yorkshire barely negates his point, and Glenn is grateful that Lee didn't sit out those final months in comfort at Elland Road.
"He has certainly not come for a ride," he says, "because we are in a highly pressurised situation at the moment, which I believe brings out the best in good players - and it goes without saying that Lee Bowyer is an exceptional player.
"I am sure he will handle the pressure of where we are in the table well, and it will help us to gather the points over the next 17 games that we need.
"He has got a genuine belief that we can get the required total of points that we need to stay up.
"We have got a game plan which is for our eyes only; he has bought into that and feels we can hit our targets, so now we have secured his services we can double our concentration, if you want, on getting the striker that we need."
And will those trademark black gloves be traded in for claret and blue ones at the weekend?
"I don't know about that but he has got his claret and blue shirt and he is looking forward to putting it on," smiles Glenn.