Bellamy is expected to leave Manchester City permanently during the transfer window after spending last season on loan at Cardiff City.
The Championship club have played down talk of a return for the Wales international, but Celtic do hold an interest in the striker.
The 31-year-old enjoyed a loan spell with the Bhoys in 2005 and his international team-mate Joe Ledley has urged Bellamy to return to the SPL giants.
However, with City rumoured to want ?4million and Bellamy's wages reportedly in the ?90,000 a week region, a deal is currently looking remote.
Lennon appeared to acknowledge an interest in signing Bellamy, but conceded Celtic are not in a position to meet the player's present salary.
"If you are talking that sort of money, then no," replied Lennon when asked if Bellamy could join Celtic on his current salary.
"It's a remote possibility at the moment, unless some sort of scenario comes up where he could come down a bit on the wages.
"He's not back from holiday yet and we'd need to know what the situation is and the proposal. Peter Lawwell is looking at it, although I'm not over-confident on that one."
Source: Team Talk
Source: Team Talk