Ukrainian Prime Minister Mykola Azarov said that upgrade would cost much less than South Stream but deliver the same results.
"As for the South Stream project, we have an alternative which we will offer to our Russian partners. The issue is about modernizing our southern gas pipelines, which will raise their capacity to the one planned for South Stream," Azarov told Russian newspaper Wsgljad. "This project will cost $1 billion, unlike the $25 billion for South Stream."
The Russian gas would also arrive at Burgas, in Bulgaria, Azarov added.
South Stream, intended to move 2.2 trillion cubic feet of gas per year from Russia under the Black Sea to Bulgaria and then on to Western Europe, gets gas from Russia and is backed by Italian company Eni.
That Ukraine would like to see South Stream stopped is no surprise: The pipeline, to be unveiled in December 2015, is aimed at bypassing transit countries Belarus and Ukraine.
Around 80 percent of Russia's gas exports to Europe are sent through Ukrainian pipelines. In the past years, constant confrontation between Kiev and the Kremlin led to several gas price rows that temporarily halted energy flows to Europe, damaging Ukraine's reputation as a reliable transit country.
In the aftermath of the first gas conflict, two major Russian-European gas pipeline projects -- South Stream as well as Nord Stream under the Baltic Sea -- were jump-started in a bid to bypass Ukraine and deliver Russian gas unilaterally to Europe.
Yet the tide has turned in Russian-Ukrainian ties. Viktor Yanukovych, a pro-Russian figure, took over as president of Ukraine early this year, and relations have since considerably warmed.
Yanukovych hopes that the improving relations help bring about new deals to modernize the Ukrainian gas transport system. Ukraine doesn't have the money to do it alone, as its economy is in shambles and the national budget overstretched. If South Stream is built, then modernizing the pipelines wouldn't make too much sense for Russia, which could shoot most of its gas exports through South Stream and Nord Stream.
Ukraine will try everything in its power to maintain its role as a transit country, and that will include trying to convince Russia to drop South Stream.
Yet the Russians are likely to press ahead -- also because Europe has launched Nabucco, a competitor pipeline.
The proposed 2,500-mile pipeline would stretch from Azerbaijan to Austria via Turkey and is aimed at breaking the Russian domination of gas import routes to Europe. Nabucco would be designed to carry 1.1 trillion cubic feet of natural gas per year to Europe.