"I am asking Yuriy Boiko to finish the talks shortly, within the next seven to 10 days," Yanukovych told a Cabinet session.
The prime minister said the price for Russian natural gas next year should not exceed $150-$160 per 1,000 cubic meters, echoing President Viktor Yushchenko's earlier remarks.
Ukraine currently pays $130 per 1,000 cubic meters for gas pumped from and via Russia. Media reports have suggested that in 2008 the price could appreciate to $180.
Yulia Tymoshenko, a former prime minister, is likely to soon replace Yanukovych and form a new government after the pro-Western coalition won snap parliamentary elections last month. The country's parliament, the Supreme Rada, resumes work in November.
Moscow's relations with Kiev saw a downturn during Tymoshenko's brief term as prime minister in 2005, and analysts have suggested the Kremlin could use gas as a bargaining chip in potential political disputes with Ukraine's new government.
Russia's state-controlled gas monopoly Gazprom demanded Ukraine pay off its gas debt and threatened to cut supplies on October 2, just a few days after the elections. The deal was reached in a week, but it revived memories of a bitter pricing row between Moscow and Kiev in early 2006, which affected gas transits to Europe.