The 33-year-old has just completed his Olympic Games duty with Great Britain but is now keen to return home for the final years of his career.
"We have been in talks with him and Cardiff," said Rodgers.
Rodgers revealed he spoke to Bellamy during the early stages of the summer, where the striker revealed his desire to be back closer to his family.
"I had a really good meeting with Craig before I moved up here," said Rodgers.
"He is a big Liverpool supporter but I also understand his thinking.
"He is 33 and has travelled around the country all his life, so there are compassionate reasons.
"We will look at it but we will wish him all the best and move forward."
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