"Ukraine is experiencing serious problems with payment," Alexei Miller said on Russia's Vesti channel in comments carried by the Ria-Novosti news agency.
Ukraine has until January 11 to pay for gas, according to Gazprom, which has cut off supplies to the country over unpaid bills repeatedly in the past.
"We are hearing and seeing that Ukraine is experiencing very, very serious problems in paying for supplies of Russian gas for December," Miller said.
"We estimate the situation with the payment for the December supplies of the Russian gas as very serious," Miller added.
Gazprom spokesman Sergei Kupriyanov, speaking to AFP, said Ukraine would find it hard to cover its next gas bill after the International Monetary Fund turned down its request for a new loan tranche of $3.8 billion dollars.
Asked what will happen if Ukraine fails to meet the January 11 deadline, Kupriyanov said Gazprom would act "in accordance with the contract," a phrase the company has used in the past when turning off supplies.
"At the current moment there are no objective reasons for a new crisis," Kupriyanov added.
Ukraine's energy company Naftogaz declined immediate comment.
In January, a pricing dispute between the two countries resulted in Russian gas being cut to much of Europe for two weeks as winter temperatures plunged.
Prime Minister Vladimir Putin has repeatedly said that Russia will cut gas supplies to Ukraine again if the struggling ex-Soviet nation fails to pay for its energy supplies.
If Gazprom acts on its warning, the cuts would come amid intense campaigning for Ukraine's presidential election on January 17.
Last month, Putin and his Ukrainian counterpart Yulia Tymoshenko vowed at a meeting in the Ukrainian resort town of Yalta that there would be no repeat of the gas crisis in 2010.
Ukraine has been hard hit by the global economic crisis which triggered a massive slump in its export-dependent heavy industrial sector.
The IMF extended a $16.4 billion dollar credit in November 2008 to help Ukraine weather the downturn, by far the country's biggest source of foreign income in 2009.
So far the government has received a total of $10.6 billion dollars but the IMF is withholding the next tranche of $3.8 billion dollars due to concerns over political infighting in the run-up to the presidential election.