He also reveals that he has assured Nigel Winterburn that Vladimir has not come in as a direct replacement for him.
Glenn stresses that the deal is not yet signed and sealed - but he would like to get the paperwork completed in time for him to be in the squad at the weekend.
That would depend on a medical being passed and international clearance being processed, but Glenn is hopeful and says: "We are trying to complete the deal in the next day or two. If we get the green light, which we hope to, it is a question of whether we can get him registered in time to be involved against Leicester.
"I will only know he is our player when the ink has dried - we think we are there and it is just a question of whether we can get it all tied up in the next day or two.
"He is one of those players that we have looked at over the past four to six weeks. I myself went to see him play in a Champions' League game in Rotterdam before Christmas where he had a very good game against Brett Emerton and we have watched him another four or five times, and all of the reports have been decent.
"In Holland that night he delivered some excellent balls into the penalty box.
"With the squad so small and the games coming in thick and fast we are definitely going to need more bodies, and he has got just the experience I was looking for.
"His pedigree is decent - you have to be a very good player to play for Sparta Prague, and they are having a very good campaign this season in the Champions' League, where they are through to the second stage, and he played for them in the competition last season as well.
"I thought he would be a good addition to our squad because he is versatile. Vladimir can play left back, left wing back, wide left in a 4-4-2, and they are the sort of players, when you are operating with small numbers, that you want because they can play in different positions.
"He is predominantly left footed and Sparta Prague rate him highly enough to use him on all set plays in the attacking third for free kicks and corner kicks."
Vladimir has foregone the chance to continue playing in the Champions' League to come to Upton Park and, while that might puzzle many, Glenn explains: "That was very much in his mind as to whether he came now or at the end of the season, and any player would want to be in it.
"But we needed to add him to our squad now. I have got a number of players on four bookings and I am very hopeful Vladimir is going to be the first of at least three new signings, so somewhere in the next week or two we are going to be adding to the squad again at least twice more.
"At 27 he wanted the opportunity to play in the Premiership - players around Europe are very aware of the attraction of playing in the Premiership, and not only that, he wanted to see a different culture, learn English, and add another string to his bow."
There will be more transfer activity in the weeks to come, and Glenn adds: "I'm not expecting too much movement on the outgoing side. I can't possibly do that because I haven't got the numbers.
"Irrespective of what happens we need to hopefully to get two more in in the next two weeks. I have targeted two or three players that we want to bring in and with hard negotiation maybe we will be able to do that.
"To all intents and purposes there is little if no money to spend so we really are having to work hard on the negotiating side, which I don't mind - I never want to be seen to be paying over the odds for anybody.
"The way I have been brought up us as a person is that you never pay the asking price anyway - you negotiate hard and get the price down, and we need to do that at the moment because we have very little money to spend in the transfer market.
"Let's hope there is still room for manoeuvre and we can get another two players in to give the squad a little bit of strength in depth, which we just haven't got."
As for Nigel, Glenn reveals: "I have spoken to Nigel today, because, funnily enough, he came in for a general football chat and it was an opportunity for me to say that Vladimir could be coming in to the club and I told Nigel he is a very versatile player.
"Just because he is at the club doesn't mean Nigel isn't going to play for us. I'm sure Nigel has many games left in him for us between now and the end of the season.
"I haven't signed Vladimir just to play left back. I'm sure he will play in all the three positions I have outlined already.
"Nigel has done ever so well for us this year and he accepts the situation.
"I think, to be honest, the players themselves would rather have some more players in the squad - it is not good for them not to.
"Players are not silly and they know the situation, none of us sit comfortable when we have so few numbers."
Vladimir will be Glenn's sixth signing since taking over, and he says: "Tomas was the last one and it seems a long time ago but that is how careful we are trying to be.
"To have brought Vladimir into the club we have covered thousands and thousands of miles and looked at 20 or 30 players.
"Some we would have liked but they were too expensive, and some we didn't fancy at all.
"Hopefully we have got this one right and he will have a good career at West Ham. He did pop over to see us play against Arsenal and he liked the training ground and the new stadium.
"He is very enthusiastic about joining us, and I think he went back to Prague quite excited about the prospect. At that stage it was far from being certain but now we hope we will be joining us in the next couple of days.
"He will be a bargain if he comes up to what we think he will be but it is all about how he can adapt because I'm sure that league football in the Czech Republic is not the same as here.
"But so far, players that have come to the Premiership from that part of the world have done very well. We are obviously pleased with our own Tomas Repka and Smicer and Berger have been very successful at Liverpool.
"Ludek Miklosko, our own goalkeeping coach, had a terrific career at West Ham.
"They are a tough group of people in the Czech Republic and Slovakia, which of course was originally one country.
"It is good for Vladimir that Tomas and Ludo are here so he will be able to converse with those two and he is very keen to learn the English language which I'm sure he will do fairly quickly."
All but one of Glenn's signings have been regulars this season - the exception being Laurent Courtois, who signed on a free transfer from Toulouse, and Glenn adds: "Laurent has done really well. In the early part of the season he played his part in us getting points and I'm sure people will remember his performance against Newcastle in particular.
"I think Laurent accepts that Trevor, Michael, Joe, and Don make up our first choice midfield.
"It is up to Laurent to try to break into that, and I'm sure he will play some more games for us this year but for someone that cost us no money he has proved he is up to the standard when required.
"I am concerned about picking up any injuries or suspensions, so I hope this is the first of three signings over the next couple of weeks and we will be working as hard as ever to try and get it right."