Speaking at a press conference, Lennon said the club are currently in talks with both City and Bellamy’s representatives over a loan deal.
The 31 year-old striker is eyeing up a move away from Eastlands as he feels he is unlikely to be included in Roberto Mancini’s 25-man squad for the coming season.
Bellamy has already turned down a move to Wolfsberg and revealed he may quit football if he cannot find a suitable switch, but Lennon believes he can offer the Welshman a way out of his quandary.
"When you see someone of the calibre of Craig and the fact that he's not in the 25 and he's looking to go out and play football then we feel it's something we can't try and miss out on," Lennon told reporters at a press conference on Thursday.
"We've been speaking to his representatives, we've been speaking to Manchester City, so how far down the line we are will be down to Craig obviously.
“But the advantage we have over a lot of teams is that we're not in the Premier League and he's been here before.
"He enjoyed his time here and made a huge impact on the game up here and he's got a real connection with the supporters."
"I thought he was their best player last year and I thought outside Chelsea and Man United he was probably the best player in the Premier League."
Bellamy joined City for around £14 million in January 2009. The move would see him reunited with the club he scored seven goals in 12 appearances for in 2005 while on-loan from Newcastle United.
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