Italian oil and gas group Eni
The amount is in a range of $1.0-1.4 billion, Scaroni said in a meeting with reporters.
Iran has been paying back Eni for decade-old deals with oil for years. Three years ago Eni was owed around $3 billion in oil.
The long-simmering confrontation between the West and Iran over its nuclear programme entered a decisive phase in January and the United States and Europe devised new sanctions to prevent Tehran selling oil.
EU governments with existing contracts to import crude from Iran can continue with them until July 1.
Scaroni said Eni was exempt from the embargo since it was the subject of a special rule covering oil it receives from Iran as payments for investments already carried out.
Eni has been reducing its purchases of Iranian crude, which come on top of the amounts of its own oil which the group withdraws under the special rule, Scaroni said.
He said the company is looking for alternative crude suppliers, such as Saudi Arabia.
Scaroni said the Italian refining sector had been traditionally heavily dependent on Russia's Urals crude and Iranian oil, noting the loss of Iranian imports would be rather painful for Italy.
Capacity at Eni's loss-making refining division can be reduced by temporary halts of operations if markets remain depressed but, bound by an earlier agreement with trade unions, the group would not close down refineries until 2014, Scaroni said.
If the market remains weak we can reduce capacity. But we have a commitment not to close any plants until 2014, he said.
Scaroni would not comment on whether Eni would shut down any of its refineries beyond 2014.
He said Eni will restart its 70,000-barrel-per-day Porto Marghera refinery near Venice in early May as planned after suspending production in November for six months.
Eni's refining and marketing division has lost 1.2 billion euros over the past three years, leading to speculation the group might downsize its refining operations.
(Reporting by Stephen Jewkes and Svetlana Kovalyova; editing by Jason Neely)