That he might also be wearing the three lions of England again is a view shared by Glenn's counterpart last weekend, Sir Bobby Robson - who also tried to sign him when the January transfer window opened a fortnight ago.
"It has been brought to my attention, through talking to managers in the Premiership, how many of them would have liked to have made the Lee Bowyer signing," says Glenn.
"You would have thought that the reaction he has got since he has signed for us would have happened wherever he signed but I think there comes a time when, after people have been allowed to have their say - and they have certainly had their say - we have to move on and allow Lee Bowyer to get on with his football.
"After what I saw for 90 minutes on Saturday I know he is going to be a great asset for us. I know he will bring out the best in other players in the squad, and there has been a real positive reaction towards Lee from the rest of the players.
"He has created the reaction that you want a new player to create - and when we get a striker through the door he will create the right kind of reaction from the rest of the team as well.
"Everyone is allowed, in the free world, to say what they feel they should say, and, as I said, in the case of Lee Bowyer signing for West Ham, everyone has.
"Now comes the time for us to move on and let Lee concentrate on his football, which is the reason he is here and wanted to come to us.
"In the seven days or so around his signing everyone has had an opinion - we have seen what the opinions are.
"Now it is time to talk about Lee Bowyer playing football for West Ham.
"For the people that have had their say, if they are fair people, it is time for them to move on as well - that is the way it should be.
"We live in a free world, there is a time and place for everything. We have seen the opinions, we have listened to them, we understand what has been said, but it is now right that we let Lee carry on with his football.
"Everyone in the game, football people, knows that Lee Bowyer is an excellent acquisition for West Ham. Some people have come out and said it, some have kept quiet - and that is their right.
"But too many respected football voices have said he is a terrific football signing for West Ham - and that is it in a nutshell.
"He has been selected for England recently and with his best years ahead of him I am sure he will play for England many more times.
"Someone told me one or two commentators have suggested he is not the player other people think he is, but the important, respected football people, all say he is an excellent talent."
Glenn believes, if you'll pardon the pun, that Lee has more than one string to his bow, and adds: "He has got many different abilities - people always drag up the aggressive side of Lee Bowyer's game, but there is much more to Lee's game than being an aggressive midfielder - that is only part of it.
"I saw him playing for Charlton's youth team when he was 16 and he has moved on as a player in terms of technical ability unbelievably.
"That is still going to get better and better as he gets older.
"He scores goals, he can see passes, he tackles well, and has as good an engine as any midfielder in the country.
"Between the two penalty boxes he can run as hard and as far as anyone."
Glenn was pleased with Lee's debut and adds: "It is amazing when you think he only had a couple of days training in the previous month. We thought he would do well to last 70 minutes but he was going stronger in the last 10 minutes than he was in the first 10.
"He was allegedly going to Liverpool for £9m last summer and Gerard Houllier is one of the most respected managers not only in this country but across Europe.
"His reputation spreads right across Europe and he was prepared to pay that money for him - and I am sure he would have been a great signing for Liverpool.
"But we have been fortunate enough to sign him on a short term contract, and we want Lee to produce his best football for us over the next 16 games - and I am sure he can do that for us.
"It is time now to concentrate solely on football."
Glenn feels that there has been an unfair portrayal of Lee in some quarters, and adds: "He has been very well received by everyone at the football club. Everyone has got on extremely well with him and, as Terry Venables said on Sunday, I think, he has done many things that go completely unnoticed.
"He doesn't go looking for the publicity that says he has done many good things but Terry has mentioned that he has done a lot of charity work.
"But he doesn't advertise that because he is not that kind of lad.
"All the players have made a fuss of him and he has settled in remarkably quickly.
"And the more we get to know him, and the more he gets to know us, it is only going to be of benefit when he is out there playing."
Newcastle boss Sir Bobby Robson certainly admires the signing of Lee - he would have snapped him up himself if he had been able to.
"Glenn Roeder and the club won't have made the decision without a great deal of thought," says the former England boss.
"Glenn is one of the youngest managers we have in the Premiership yet he has made a strong decision.
"We are all egotists. We all think we can handle the difficult players - that is why we buy them."
"It would have taken a strong decision from a guy like me or even Howard Wilkinson who tried to sign him, and Howard has been in the game far longer than Glenn.
"Bowyer has to get on with his life, and what he needs is other people to help him to get on with his life.
"You cannot just push him aside - and West Ham have the faith, the courage and the confidence that this is the right thing for them.
"He needs a guiding hand and he has got one there, and that speaks volumes for West Ham - they are giving the boy a chance to re-establish his football fame at a fine club in London.
"Was the boy proven guilty? No. Therefore the boy needs a chance, and West Ham are giving him that chance - and we should support that and let him get on with his life.
"Let's look ahead - West Ham is his club, his scene, it is where he was brought up.
"He has come back to his roots, and your roots are very strong - that is why I am very happy where I am, back at my roots.
"It gives you more determination because you are at home, back where you went to school and played your young football, where most of your friends are and where you are happy.
"The London scene has a lot of big clubs with the likes of Arsenal, Tottenham, Chelsea and West Ham - and he is among his own folk."
Robson thinks that Lee can resurrect his international career soon and adds: "I saw him play for England against Portugal at Villa Park last year when Alan Smith got all the rave reviews - and I thought Lee gave a very pleasing performance.
"He is 26, so he has got four great years ahead of him as an England international - Bowyer is an international player.
"As a player I think he is fantastic, and they tell me he is a fantastic boy. I don't know him as a person because I have never spoken to him, but as a player he is a fine player.
"He hadn't played for a month on Saturday, so his match rhythm would be lower than normal, but I think he can pick up the pace and rhythm of his game in another match or two.
"After that he'll be the player everybody thinks he is - and we all think he is a very good player."