The Northern Irishman hopes to speak with representatives of the Premier League club this weekend when both teams compete in the Dublin Super Cup.
Lennon told the Daily Telegraph: "There is interest, but it is dictated to by finances. I hope to catch up with [City] while they are here and see if we can take it from there."
Frontman Bellamy became a popular figure among the Hoops faithful during a successful loan spell in Glasgow six years ago when a Newcastle player.
The 32-year-old was loaned out to Cardiff last season but has since returned to City, who further bolstered their attacking line with the acquisition of Argentina striker Sergio Aguero on Thursday.
Source: Team Talk
Source: Team Talk