Porto announced on Sunday that they had agreed to sell Cissokho to Milan but a dental problem uncovered in a medical on Tuesday prompted the Italians to renegotiate the terms of the transfer.
Media reports said the original fee agreed was about 15 million euros.
The Serie A club's chief executive Adriano Galliani said earlier on Thursday that doctors had found a dental problem that causes muscular trouble and which could deteriorate.
It is a setback to Milan's bid to rebuild following the departure of coach Carlo Ancelotti for Chelsea, the transfer of playmaker Kaka to Real Madrid and the retirement of captain and fullback Paolo Maldini.
They are also hoping to buy VfL Wolfsburg's Bosnia striker Edin Dzeko. The German club have recently given signals they may be willing to open talks after initially saying the 23-year-old was not for sale.
NEWS: Cissokho finally seals Milan deal
NEWS: Dental dilemma ruins Cissokho deal?
NEWS: Milan seal deal for Cissokho
