"The signal that we are in effect getting from our Ukrainian colleagues is that the situation with payment for gas from Ukraine is going to get worse," Miller was quoted by the state-backed Russian news agency RIA Novosti as saying.
Miller said Ukraine hasn't yet paid its August natural gas bill of $882 million. Gazprom cut natural gas supplies to Ukraine most recently in 2009 because of payment concerns.
The Ukrainian government said it pays some of the highest prices for natural gas among Gazprom's customers in Europe.
Ukrainian Prime Minister Mykola Azarov said there were issues with Gazprom but nothing extraordinary.
"There are problems, but they are not critical," he said. "The government has this issue under control."
European countries get about 20 percent of their natural gas from Russia and the majority of that is delivered through Soviet-era pipelines in Ukraine.
Celebrity Families of 2014 [PHOTOS]