The centre-back was left out of the Anfield club's squad for Thursday evening's Europa League qualifier against FC Gomel and that sparked extra speculation.
Liverpool had rejected two bids from City for Agger and further reports had since suggested the Dane handed in a transfer request.
Agger's agent, Per Steffensen, on Thursday night did little to calm the situation by announcing his client was 'not injured in any way' before the Gomel game.
But Rodgers is adamant the injury-prone centre-back was only absent in Belarus due to fitness issues, as he said: "The plan was always for Daniel to stay behind.
"Everyone knows his history of injuries. He came back to pre-season training after everyone else and is still not up to speed.
"He is fit but I have to make sure he is up to speed before he plays, because everyone knows his history with injuries."
Agger is under contract with Liverpool until the summer of June 2014 and earlier this summer he admitted he would welcome the chance to discuss a new deal.
City could therefore find it difficult to convince their Premier League rivals to sell and reports have suggested the English champions are instead looking at Marseille's Nicolas N'Koulou.
