The Frenchman's current contract with the club expires at the end of the month but the two parties had been expected to thrash out an extension.
However, Flamini's representative, Helene Misserly, told reporters after Wednesday's talks that an agreement over a new deal has yet to be reached.
"The meeting was helpful for making our position clear, and to understand that of Milan," the agent explained to reporters. "But in order to reach a decision, we will need to meet again. Flamini is happy at Milan, but it's not certain that he will stay there."
Flamini, who has three France caps to his name, joined Milan from Arsenal five years ago.