His patient wait for a striker is well documented and, following Spurs' decision to allow Les to talk to West Ham, is likely to reach fruition sooner rather than later.
"We are hopeful of getting a deal done and Paul Aldridge has been discussing it with Daniel Levy at Spurs," says Glenn.
"There has been a breakthrough and we feel positive of a favourable result.
"If Les passes a medical we would look to register him in time for the trip to the Valley."
Les, with two goals in five starts this season following 15 from 33 appearances last term, will not be eligible to play in Sunday's FA Cup encounter with Manchester United, however, as that would have required him to have signed a week before the game.
But Glenn would like to add someone at the other end as well if he can.
"I am very confident with the midfield players we have got when everyone is fit but ideally - and this is the difficult bit - we would like to bring in another central defender," he says.
"But everyone is finding it hard to find a central defender of the quality you would want."
He says competition is fierce and reveals: "It is not just us looking. I am aware of about eight Premiership clubs looking for a central defender for the remainder of the season.
"They just don't seem to be out there as far as loans are concerned.
"Matthew Upson might well be going to Birmingham, and he is a very decent young central defender, but he is going for a transfer fee and we can only get involved in loans.
"We won't stop looking until the window shuts but with 11 days to go we are finding it increasingly difficult to find a central defender of the quality we want - but we could really do with a dominating centre back that can do it in both penalty boxes.
"They are like gold dust, but we are using all of our network - like other clubs are.
"If three or four central defenders had been signed by Premiership clubs I would be very disappointed that we would have missed out, but there hasn't been.
"We will keep looking; you never know, something might just well turn up."
* Steve Lomas misses the Premiership game against Liverpool at Upton Park on February 2nd as a result of his sending off at Highbury on Sunday.