Yildiz was quoted by Iran's state-funded broadcaster Press TV as saying energy demands at home could make Iran a reliable energy partner.
"We have discussed how we could increase our imports to 700 trillion cubic meters and the price mechanism needed for that," he said Tuesday.
He didn't offer an indication on current levels of imports.
Iran has looked to Turkey as a potential transit option to get its natural gas reserves to European countries. In the past, members of the European Union have expressed reluctance given the economic sanctions pressure on Iran.
Press TV reports a deal from the 1990s on natural gas makes Turkey one of Iran's more important regional clients.
Iranian President Hassan Rouhani told delegates at the World Economic Forum in Davos, Switzerland, last month an interim nuclear deal with Western powers could make Iran an attractive energy investment. U.S. officials, however, have said Iran is not open for business.