But he has "never heard" of Monaco defender Julian Rodriguez, with whom he has been linked, and has no intention of signing Hakan Sukur, the Inter Milan striker.
Glenn is certainly keeping busy as he looks to improve the West Ham squad, and says: "There aren't enough hours in the day to be honest.
"The search will continue to go on until I get the sort of talent that will make us a better team.
"Once the money is gone, it's gone, and even though it is a decent amount of money it is proving difficult to spend to bring in the kind of player that we are looking for."
While newspaper reports would have him spending £5m or so on Sukur, who says he wants to come to the Premiership, Glenn insists the priority is midfield and defence.
"It has to be said that when you strip everything away and look at the central defence we've lost Margas, Stimac, Stuart Pearce, Rio Ferdinand - four experienced centre backs that have left.
"It now makes us particularly light in that position.
"We've lost Frank Lampard as well but you have to say of the six or seven players that have left Frank was obviously the key one who we would have liked to have kept at the club.
"Then obviously Igor, but two or three of the others that left the club didn't really play a part anyway."
Talking of specific players, he adds: "Asuar is up for a week with us training - I would not describe it as a trial because he is a senior player.
"We haven't even gone down the road of thinking money; we would only do that if we wanted to do anything, but we will decide at the end of the week.
"I have not heard of Rodriguez before, and as for Sukur, the answer is 'no'.
"We are sitting targets to be linked with everyone, and it is annoying.
"Agents know we are in the market and they are trying to shift their players via us.
"Obviously our supporters are waiting for the next couple of signings - and I am certain they will happen.
"But picking up the phone and signing a player in 24 hours just doesn't happen any more.
"Sometimes there are two or three agents involved and simply because of that a deal can take up to seven or ten days."
Glenn will take a close look at Paul Ashtonhernandez, Mirandinha's son, however, and reveals: "He came in last week to visit us after being in Holland and France.
"He is a striker like his dad but a lot bigger though he seems just as quick as Mirandinha was.
"I played with him at Newcastle and I know he had lightning pace - and the lad appears to have inherited that.
"He is obviously only a young boy, but because of my friendship with Mirandinha he came to us first before he goes anywhere else.
"I would have thought we would be in pole position there as well and we can keep him as long as we want to.
"He plays his part in the coaching practices and is enjoying being with us as much as we are enjoying watching him play at the moment.
"But there is going to be no decision made immediately and if we took him we wouldn't consider him a major signing with respect.
"That is because he is a young boy trying to make his way in the game.
"I think the important thing for any player from abroad is that you get the first look.
"We've got that, but we will only keep him if I genuinely thought that he would be pushing for a place in a year or so.
"If he couldn't do that it wouldn't be fair to us or him to keep him."
Mirandinha scored around a goal every other game when he played with Glenn at Newcastle, and has said: "I trust Glenn completely so this was obviously the club to bring him to.
"I'm sure he will follow in my footsteps by playing for Brazil - and he is available on a free transfer."
Glenn adds: "He'd have to get used to the English game and the pace it is played at, so some polishing up would have to be done.
"But there is nothing to be hurried or worried about; he's enjoying his training, he's a credit to his father in the way he conducts himself, and he is not a problem to have around the place."
And he will use the Peterborough game to once more run the rule over Lauren Courtois, who played against Bishops Stortford on Friday night.
Reveals Glenn: "I thought he did quite well and we will take another look at him.
"Joe will not be risked, though he will be fine for the game at Stevenage on Monday, and that will give Lauren the opportunity wide on the left to impress; that is his natural position.
"There were two or three clubs that watched him at Bishop that were sufficiently impressed with him to offer him a trial if we weren't taking another look.
"But we are in pole position and we will talk to Lauren on Wednesday morning after the game.
"He came through the youth team with Fredi Kanoute at Lyons and there is a big friendship there, and he was a regular at Toulouse last season.
"He is only 22, and is not the tallest, but he is strong and sharp and has shown us in training what a good left foot he has got.
"Hopefully he will be supplying some crosses into the box for Fredi at Peterborough.
"I would describe him as a wide midfielder rather than a winger - there aren't too many of them around these days.
"The Peterborough game should be a better test for him."