Ankara plans to pass the proposal on to private companies, Yildiz told reporters, adding the offer would require an investment of $100-200 million.
He did not give other details.
An earlier project for Turkey to develop three large gas fields in Iran had been dropped as the two neighbours failed to agree on the terms, Yildiz said.
He explained Turkey wanted to both use and sell on to third parties part of the gas to be produced but Iranian law made that impossible.
"The decision was made purely on technical grounds," he said, rejecting suggestions that international pressure on Iran over its nuclear activities had had any influence.
Yildiz stressed that UN sanctions imposed on Iran did not hinder cooperation in energy projects with the Islamic Republic.