Although Sven's fellow countryman Dime Jankulowski was on trial at Upton Park last week, Glenn's preferred option is the 38-year-old, who has played a record number of games for his club but was contemplating retirement now that the Swedish season has ended.
"We haven't actually signed him yet," says Glenn, "and haven't officially done anything, but in principle he wants to come and stay with us.
"To all intents and purposes we will take him for four or five months.
"He certainly played well against Ipswich in the UEFA Cup this season and has got a lot of European experience.
"Glenn Hoddle signed a 42-year-old goalkeeper last week (Dave Beasant) and age isn't a problem if you are still fit and able to do a job.
"But it needs to go through first before we can say he is our goalkeeper."
Of the other recent trialists at the club, defender Petter Olsen has returned to Norway, while his Brann Bergen team mate, striker Azar Karadas, is still training with the Hammers.
Glenn, meanwhile, has denied being interested in signing Leicester midfielder Robbie Savage, and says: "As far as Robbie Savage is concerned I haven't contacted Leicester about him; Dave Bassett has said that we haven't made any approach and he is telling the truth.
"The amount of money that was quoted anyway is such that I'm not in a position to do anything even if I wanted to.
"But he is very much a Leicester player, very committed to their cause, and I don't know where the story came from - it is very strange."
As for the injury to Fredi Kanoute, which ruled him out against Charlton, Glenn says: "Fredi has a slight hamstring problem but we are hoping it is not going to be long term.
"We will have to wait and see, but he is doubtful for the game against Tottenham.
"It goes without saying that it is good Paul Kitson came through the Charlton game; I only took him off towards the end because he was starting to feel tired and we had the little fellow champing at the bit to come on."
Glenn acknowledges that when Fredi is fit, he will have quite a selection poser up front, but says: "It is the better type of headache to have; the headache you don't want is not having enough players.
"At the end of the day, no matter how well you prepare players, they have got to have the ability when they cross the white line, and having Joe and Steve back was a terrific bonus."
Looking at the Charlton game in more detail, he says: "It was a very tactical match: we started with 3-5-2 and Alan said after the game he was certain we would be 4-4-2, so they worked on that all week only to find very early on that we were playing 3-5-2.
"Paul Kitson scored early on and we were on top, so it was a complement to us that they changed their shape to match us up so we were both 3-5-2.
"Then we find ourselves 3-2 down, so we make a tactical change and go to 4-4-2, which caused them problems as we went 4-3 in front with both Joe and Steve playing major roles when they came on.
"Steve, as always, was full of energy and one tackle in particular must have given him great confidence as it was on the knee that was injured.
"He came through it with flying colours, he used his voice when he came on, and his experience was put to good use.
"Joe was the Joe we all expect but because of his foot problems he hasn't been able to play like that this season.
"He was full of life and full of energy; he ran with the ball well and passed the ball well, and it was great to see him on the pitch.
"All the time his physical fitness will get better and better."
The result, though, was an irritation, and Glenn admits: "There were plenty of disappointed people at the training ground the day after; we had the three points and we let it slip on a poorly defended goal.
"Even if the execution was terrific, we had two opportunities to clear it and didn't take them.
"We looked very good at times when we were attacking but there is a lot to work on and we need two good days of training on Thursday and Friday before facing Spurs."