Rodgers: Bellamy set to leave Liverpool
"We've been in talks with him and with Cardiff, in terms of a possibility of him going back there," Rodgers told a news conference broadcast by Sky Sports.
"It's not him crying wanting to leave Liverpool, it's more compassionate reasons really."
Rodgers said Bellamy wanted to be with his family who still live in Cardiff. "He's 33 years of age and he's travelled around the country all his life while his family has been based elsewhere," he said.
Bellamy, who represented Britain at the London Olympics scoring once in four matches, has already spent time at Cardiff going on loan in 2010-11 after falling out with management at Manchester City.
He has played for seven clubs, not including loan moves, and previously joined Liverpool in 2006 before signing again on a free transfer in September last year.