The Wales international has travelled to Cardiff for further discussions and looks set to rejoin the Bluebirds on a permanent deal.
The Championship side have been chasing Bellamy since the end of last season, with manager Malky Mackay confirming his interest in the 33-year-old.
Bellamy, too, seems keen to re-sign for Cardiff, who he played for in 2010-11 on loan from Manchester City, and is now in the Welsh capital to negotiate a permanent contract.
The former Newcastle United and Blackburn Rovers forward has also attracted interest from Queens Park Rangers.