The Bhoys are keen to bring the Welsh hitman back to Parkhead, either on a temporary or permanent contract, following his loan stint there from Newcastle in 2005.
City and Celtic were thought to be in negotiations over a potential move, with Hoops manager Neil Lennon having confirmed his interest in the frontman.
However 32-year-old Bellamy, who has a year to run on his City contract, has made it clear he has no interest in rejoining the Scottish Premier League giants.
The Welshman had also been linked with a loan move to Cardiff this summer, where he spent last season.
But he has previously ruled out signing for any club on loan, stating his intention to see out his contract at the Etihad Stadium should a full-time deal fail to materialise.
Bellamy's wages are likely to prove a stumbling block in any potential permanent deal, but it appears unlikely that Mancini will be able to find a place for him in his star-studded side this season.
Striker Sergio Aguero has recently arrived from Atletico Madrid as the natural replacement for Carlos Tevez, who is expected to leave this summer, while Mancini also has Edin Dzeko, Mario Balotelli and Emmanuel Adebayor at his disposal.
The manager left Bellamy at home for City's pre-season trips to the USA and Canada and Ireland this summer, suggesting the former Blackburn and Liverpool man will not figure in his first-team plans.