Officials from Italy‘s ENI and Frances Total have met with President Nicos Anastasiades in recent weeks to discuss exploring the blocks.
The Cypriot government said on Friday it would appoint a team to negotiate contracts with the winning companies.
US firm Noble Energy made the first gas find off Cyprus in 2011. The Aphrodite field is thought to contain over 125 billion cubic meters (4.5 trillion cubic feet) of gas.