If Kiev agrees to the deal by the end of Saturday, the current price of $50 per 1,000 cubic meters will remain until April, when it will rise to $230, the BBC reported.
The BBC said if no agreement is reached, Russian gas supplier Gazprom plans to turn off the tap Sunday morning.
In response, Ukraine has said it wants further talks.
Russia currently supplies Ukraine with about 30 percent of its natural gas needs in a tradeoff for the pipeline going through that country.
Russian President Vladimir Putin made the new offer at a meeting of his Security Council.
Russian officials insist the standoff will not affect supplies to the European Union, but 80 percent of its exports pass through Ukrainian pipelines, the BBC said. The EU receives about 20 percent of its natural gas from Russia.
Germany alone gets more than a third of its natural gas from Russia through Ukraine.

