Cardiff have been chasing Bellamy’s signature with Malky Mackay previously confirming his interest in bringing the forward back to the club.
It is understood Liverpool are reluctantly willing to let the Wales international leave Anfield for personal reasons.
Bellamy played for home-town club Cardiff on a season-long loan in 2010-11 after finding himself out of favour at Manchester City.
The 33-year-old joined Liverpool from City on a free transfer last summer and impressed during his second stint at Anfield.
Bellamy, who impressed for Team GB at the Olympics, has also attracted interest from Queens Park Rangers with Mark Hughes keen to be reunited with his compatriot.
However, QPR are facing a losing battle to land Bellamy as Liverpool are reluctant to let the forward leave to a Premier League rival and would prefer to see him move to Cardiff.
Liverpool are thought to be willing to let Bellamy return to Cardiff for free with the player keen to be closer to his family home.