It is a worrying time for Glenn as he keeps an anxious eye on personnel in the next week or so.
"It is vital - absolutely crucial - that all the internationals who go away arrive back at Chadwell Heath next Wednesday and Thursday fit and ready to play at Southampton," he says.
"I want everyone fit. People might say that gives you selection problems but I don't see that as a problem - I just want to be in that position to select from everyone being available."
Another thing he can do nothing about, of course, is what other teams do, with Birmingham and Bolton both scoring injury time winners in their last fixtures against West Brom and Spurs respectively to add to the pressure.
"It was very disappointing, but as I keep getting told, and I have to come to terms with this, there is no point worrying about things that are out of our control," he says.
"The only things that we can control are our own performances and results.
"Of course, we hope other teams around us don't pick up points, just as they don't want us to pick up points.
"The feeling is mutual - that is professional sport, and that is the importance of staying in the Premiership.
"But there is nothing we can do about Birmingham scoring in the 95th minute, and there is nothing we can do about Bolton scoring in the 92nd minute.
"We can only affect our fixtures and hope that maybe there is a late winner for us up ahead that will be crucial for us as well."
As to whether he feels sides such as Aston Villa and Leeds are getting dragged into the scrap, he says: "Possibly, but I don't like talking about other teams, I just like focusing on my own team and one game at a time.
"The only game that really matters to West Ham is at St. Mary's in less than two weeks."
For the record, with seven games to go, a glance at several sides' form near the bottom in the last seven games shows that Aston Villa have picked up seven points, Birmingham nine, Bolton 11, and Leeds just three.
If, perchance, those teams were to pick up exactly the same number of points in the remaining seven games, Leeds would finish on 37 points, Bolton and Aston Villa 43, and Birmingham 44.
West Ham have earned 13 points from the last seven games, and an identical tally from our remaining matches would see us finish on 43 points.
Obviously, the notion that sides would necessarily continue in the same way is fanciful, but it does, perhaps indicate that initial predictions of a lower points total than normal ensuring safety are wide of the mark.
Bolton boss Sam Allardyce, incidentally, claims that 41 points is his team's target as no club has ever gone down with that total from the Premiership.
After the win over Spurs, Joe Cole said five more wins were needed, leaving the Hammers now to get four victories from the last seven games.