The player himself, who joined Liverpool for £10m, claimed that, amongst others, West Ham wanted to buy him.
But Glenn insists: "That one is a non-runner because we don't have those funds - and neither did we seek to raise them by selling any of our best players."
The player also named Inter Milan and Valencia as potential suitors, but Glenn adds: "Well, it sounds like we were supposed to be in good company!
"I can only assume there has been a misunderstanding, maybe involving his agent.
"Our record transfer is £5m and I have been making it crystal clear for some six months that we would not have huge funds and would therefore not be spending big sums on anyone.
"We spent money last pre-season but I knew I would not be able to do that this time around."
Glenn's big concern is the implication that, had he made a bid for the striker, he would have been prepared to sacrifice one of his stars to make the deal.
He stresses that is not the case - despite his admitted admiration for Diouf.
"He is a really wonderful talent. Our scouts saw him when he was at Lens and were absolutely right in their assessment of him.
"They liked him - and I think he will become a massive hit over here."