Revealing that Republic of Ireland international David is the man he is hoping to sign, Glenn is keen to refute the assertion made in one newspaper that, as the story claims, either Fredi Kanoute, Jermain Defoe, or Joe Cole are lined up to leave.
"It doesn't mean that at all - people are reading too much into things happening," he says.
"We have a small squad and we are trying to get the numbers up - we have lost players this summer and he is the first one in.
"I wish people wouldn't speculate, but it seems to be a national past-time.
"I hope to make more signings and it is important that every player that arrives plays a vital part in our promotion push.
"I am hoping to reach agreement with Rob Lee later in the week; he has done ever so well since joining us for training on July 1st.
"He is a respected member of the squad and he has slotted in well in the absence of Michael Carrick and Steve Lomas."
As for 26-year-old David, who started his career with Watford under Glenn, there are high hopes that he will add to the competition up front.
The emergence of Youssef Sofiane this pre-season, allied to Fredi and Jermain, plus the inclusion of David, would give Glenn four strikers to choose from - what he regards as the minimum number to sustain a challenge for promotion.
"I identified David Connolly a month ago as a potential target that will bring firepower and goals to the team," says Glenn.
"In 28 starts last year he scored 24 goals, which tells its own story.
"I know the lad, and in fact I know the man, though when I gave him his debut at 16 he was only a very young man.
"He has been on his travels with Feyenoord, where he was for four years, and he has had a couple of seasons at Wimbledon.
"His ratio of goals to games is extremely high and he is the sort of character I would want to bring to the club.
"He is fiery and strong mentally - a tough boy and he lives for scoring goals.
"He is one of those lads that keeps a mental note of exactly where and how he scores.
"In that sense there are echoes of Tony Cottee, who I believe kept a book of all his goals.
"I don't know if David does but I am sure he can tell you how he has scored his goals, and probably at what time."
Glenn also reveals that several clubs were chasing David's signature, and adds: "A lot of clubs wanted him and it has been extremely hard work to get him to West Ham. Other managers recognised his potential to score lots of goals, a number of clubs that would like to guarantee promotion themselves and one or two Premiership clubs as well.
"So it was good to beat off their challenges. Once he knew we were interested he really had the flavour to join us, and he showed a lot of patience to make it happen.
"I am really pleased to have secured his services, subject to a medical of course, and hopefully he is the first of many.
"I don't see any reason why we won't be looking back on his goals come the end of the campaign - I am sure he can continue his rich goal scoring vein with us."