"We have proposed a meeting next week brokered by the EU," Alexander Novak told Austrian daily Die Presse in an interview.
He said he spoke by phone "daily" with his Ukrainian counterpart, Yuriy Prodan, but that the "solution depends on other people … the Ukrainian government, parliament and president".
Russia in June halted gas exports to the former Soviet bloc country, demanding the new pro-Western government in Kiev pay upfront for new deliveries at higher prices.
For now gas is continuing to flow as normal through Ukraine into the EU, which relies on Russia for a third of its gas needs.
But Russia has warned there was a high risk of disruption of deliveries to Europe this winter as international tensions mounted over the Ukraine crisis.
A spokesman for the European Commission in Brussels told AFP Thursday that the "date and the venue for the meeting have not been fixed yet," adding that "several dates are being considered".
Brussels had proposed September 20 for the meeting in Berlin, but Moscow said this was not convenient.
Novak told Die Presse that Ukraine has $5.3 billion (€4.1 billion) in "gas debts" but that Moscow was not demanding repayment "all in one go".
Some of this could be "recalculated on the basis of the discounts we are offering if Ukraine accepts our price proposal — $385 per 1,000 cubic metres instead of around $485," he said.
"Gazprom would then reduce Ukraine's debt by $780 million."