Glenn, who secured the signing of Gary on Monday afternoon, reveals:
"I have had my eye on him for a while and discussions have been ongoing for seven to ten days.
"But the names being put to me were from not just all over Europe but, with some South Americans, from leagues all over the world."
Rather than bring in what might be considered a more exotic name, however, Glenn preferred to look closer to home, and says:
"I have brought in a player who cost Coventry more than £3m and who has played some 200 games in the Premiership, and knows what it is all about.
"I thought Gary would settle easily into the squad, as he knows the division and what is required.
"Some of the names were being thrown at me from all directions, and were possibly exciting ones from the biggest clubs in the world.
"But I might not have known the player and it might have taken them six months to settle in, learn the language and a new style of play, and of course adapt to the culture.
"With Gary we know what we are getting and there will be no problems with him communicating with other players, which is particularly important."
Glenn has actually played with Gary when he had him in his squad at Gillingham in the early 1990s before he moved to Peterborough for £70,000.
Glenn recalls of his player/manager days with the Gills - and Gary:
"I have seen him described as my 'pal' but I never considered him as that - he was one of my players.
"I was a sweeper playing behind two 18 year olds - him and Tony Butler, who is at West Bromwich Albion.
"He was very comfortable on the ball and took one or two chances he shouldn't have, but I can't remember him being caught in possession as the last man in defence and at the expense of a goal.
"Now, 10 years on, he is a lovely age, and he is versatile as well; like Ian Pearce, he can play right back, and he has pace and energy.
"He is as quick as Tomas Repka and Christian Dailly - another defender who is versatile and can play in midfield.
"I hope he can have a long career here, and he really adds height, at 6' 3", to our defence."
Gary's performances in the World Cup convinced Glenn that he was a worthy target, and he adds:
"He acquitted himself well in the World Cup - just think of how he did against Raul and Morientes of Spain.
"He comes highly recommended from Mick McCarthy, who I contacted about him, and he spoke in glowing terms about Gary, both as a player and a character.
"Paul Goddard spoke to an international colleague at of his at Ipswich and the message was loud and clear.
"He will make the squad stronger - I am desperate to get numbers in - but he knows he will have to fight for a place.
"I think that, for a London lad, the lure of coming to a club as good as West Ham was great.
"And he will soon be passing the 50-cap mark for Ireland."
That is certainly true; after his World Cup exploits, he is on 47 caps, having scored six times, and played in every minute of Eire's involvement in the competition.
He began his career as a junior at Charlton, but did not play league football until he went to Maidstone, and thence Gillingham.
After over 80 appearances for the Peterborough, he moved to Birmingham for £250,000 in 1996, and, less than a year later, on to Coventry for more than ten times that.
But, after years as a first team regular, Glenn Roeder has told him he will a spot at Upton Park is not guaranteed.
"It is important we have competition for places," he says, "and I have told him he will have to fight for his.
"He accepts that, and is looking forward to the challenge - and I am sure the boys will look forward to him joining us."
The signing of Gary confirms that Matt Elliott of Leicester was not on Glenn's shopping list, as reported on Sunday.
"That story was completely wrong; he has had a fantastic career for Leicester and I am sure he has got more games to play for them yet.
"We are pleased to secure the services of a younger man, one who is a suitable age."
Glenn hopes to add one or two more names to the squad before the transfer deadline, and he reveals:
"I am looking to bring in at least one more player, at the top end of the pitch, and with the budget I have got, you never know, I might be able to squeeze a second one in.
"So it is 'Gary Breen plus one' as the more likely scenario, but possibly 'plus two', depending on other things happening."