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.
He added that Porto had accepted the idea of loaning the 21-year-old to Milan with an option for a permanent move, but had not agreed to the fee proposed by the Italian side.
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.
New coach Leonardo does have one reinforcement for his back-line though -- Brazilian Thiago Silva.
The 24-year-old moved from Fluminense in January but could not play during the second half of last season because Milan already had their full quota of non-EU signings.
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
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