Cyril Nzama, a central defender from South Africa, has pleased the Hammers boss already with his fortitude in stepping off a plane and heading straight across London to train at Chadwell Heath, in a bid to prove he could establish himself in the Premiership.
But Glenn stresses that it is just a tentative examination at this stage and explains: "Cyril has come over from South Africa and his people have paid for the trip, so it was a free look for us.
"We have only seen him for one day but we will see him on Wednesday, Thursday, and Friday in training.
"He seems a very decent man and has impressed us with his mentality.
"He flew through the night, having set off from South Africa on Sunday evening.
"He arrived at Heathrow at 7:30 in the morning and was training with us at 10:30 - that is someone who is hungry.
"But of course we are only having a look, and one that guarantees no promises to the lad."
As for what eventual deal might be struck with his club, Kaiser Chiefs, for the 28-year-old who was part of South Africa's World Cup finals squad in Japan and South Korea last year, Glenn says: "We are not even thinking that far ahead - let's see what happens over the next few days."
Meanwhile, midfielder Brent Rahim, who has been on loan from Bulgarian side Levski Sofia for six months, has been released.
"We have let Brent Rahim go to Luton and we are very hopeful they will give him a contract until the end of the year," says Glenn of the Trinidad and Tobago international.
"If he can secure a contract he will play first team football - which he needs to do."
In another outward move, fellow midfielder Leon Britton has been allowed to extend his loan at Swansea until the end of the season.
Says secretary Peter Barnes: "Leon has been allowed to stay at Swansea for the rest of the campaign but he still has one more year to go on his contract."
Meanwhile, Don Hutchison will be back in training and available for the Newcastle game on Saturday following the death of his father.
"I haven't spoken to Hutch since his father's funeral on Monday; my guess is he was travelling back from Newcastle and we will see him tomorrow," says Glenn.