Highways minister Lakshman Kiriella has confirmed the discussion and said the two expressways would be leased out for a period of 15 or 20 years.
Maintenance and running of the expressway will then be the responsibility of that company, he said.
Leasing out expressways has been a success in other countries, said the minister.
He said that once a final decision is taken, advertisements would be published for competitive bidding and the highest bidder would be given the offer.
He refuted allegations by the opposition the expressways would be sold.