Kazakhstan is locked in a dispute with the Eni-led consortium over cost overruns and production delays at the huge Caspian Sea field.
"[We demand] more than $7 billion. That's for the delays," said the source, who declined to be identified.
Kazakhstan had set Friday as a deadline for the group to come up with a settlement proposal.
Eni declined to comment on the $7 billion demand.
At the height of the dispute, in September, Deputy Finance Minister Daulet Yergozhin said Kazakhstan sought more than $10 billion from the consortium.
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