"It is quiet at the moment," admits Glenn.
"Tomas Repka has stated that he doesn't want to leave Fiorentina.
"It has nothing to do with coming to England or coming to West Ham, it is just that he is apparently very happy at Fiorentina and is not looking to leave at this stage.
"But I don't think that has run its course completely and we will see what happens over the next couple of days - he is a very good player."
Although the player has been variously quoted in the past week or so saying that he wants to stay in Florence and that if he did move it would only be to West Ham, the mixed messages have only served to strengthen Glenn's resolve in getting his man.
"We will just have to wait and see," he says, adding that he commends Tomas for not flitting from club to club as many players abroad do.
He explains:
"It just shows you the loyalty he has - wherever he's been he's stayed a number of seasons.
"He was three or four seasons ar Sparta Prague and completed three seasons at Fiorentina and is saying how much he likes it.
"Some players are happy playing at one club for a number of years and if he does eventually decide to come to us it gives me encouragement that he will want to stay and play for a long period of time.
"We will just see how that develops and hopefully he will have a change of heart and still come to us."
He is not currently on international duty despite normally being a regular in the Czech team, and Glenn explains:
"The reason he wasn't involved this time is because he was in the last squad but never made the fixture, which was a friendly.
"It was all due to his situation in Fiorentina, and he was wanting to sort out his future; he didn't turn up for that game.
"The Czech coach chose not to pick him for these two games but I bet the coach wished he had picked him after losing to Iceland.
"The Czech Republic obviously missed him against Iceland because they lost 3-0 on Saturday."
Glenn says he Tomas remains his number one choice of central defender, adding:
"I'm not going to go on to another target until I am actually 100% certain Tomas Repka is staying at Fiorentina.
"While there is still a chance he might still come to us I will wait.
"I've been patient in the past, such as with Don, and it worked out OK, so I will be patient with Tomas Repka.
"He knows we want him, he knows we want to make him feel welcome and to come to England and enjoy playing for us at West Ham."
He says that it is not just his power of persuasion that could clinch the deal, but the Hammers' reputation.
"It's not just me talking to them, it is the traditions of the club speaking for themselves in terms of what our club stands for, the type of football we play.
"You'd be surprised; there are more people know about West Ham than you would think."
* Joe Cole took part in West Ham's double training session on Monday, having returned from England U21 duty.
He is ineligible to face Albania this week because he received a second yellow card of the tournament in his goal scoring performance against Germany.