Lennon is an admirer of the Welshman, who is back at Manchester City after a season-long loan at Cardiff.
Bellamy has previously stated that he would like to go back to the Championship side, but it is thought City boss Roberto Mancini is looking to sell him rather than send him back out on loan.
Celtic are taking part in this year's Europa League and the deadline for players to be registered is Monday, meaning any deal to bring Bellamy back to Parkhead, where he spent a few months on loan in 2005, would have to be completed quickly.
Lennon says that although talks have stalled at the minute, he is still hopeful of bringing in a new face before the end of next week.
"I hope to have someone in before the deadline but I can't say yes or no," he told reporters.
"I am working very hard in the background to get players in.
"It's all gone quiet [on Bellamy]. You would be interested in a player of Craig's quality but we have nothing more to add to that at the minute.
"I haven't spoken to him for a fortnight now but we will do that through his representatives."
In Friday's Europa League draw, the Bhoys were paired with Swiss outfit Sion.
The first leg will take place on August 18 in Switzerland, with the return leg a week later.
Download the Goal.com Mobile app, and the world of football will be at your fingertips and in your pocket!