The talks were originally set to conclude in October.
"I hope to put the last dot in a few days," German Gref said.
Russia, the largest economy outside the world's leading trade body, has completed bilateral talks with 57 of the 60-member Working Party of the WTO. Negotiations are continuing with the U.S., Moldova and Georgia.
Negotiations with the U.S. broke down in July over differences on agriculture, specifically meat. The development was unexpected, since the main point of contention throughout the talks had been access of financial services companies to the Russian market and the lack of intellectual property rights protection in Russia.
Moscow wanted to sign a protocol with Washington at Russia's debut summit of the Group of Eight nations July 15-17, but the deadline was moved back to October.
The U.S. currently enjoys concessions under bilateral agreements signed in 2005, which will remain in force until 2009. The agreements raise quotas on U.S. supplies of poultry meat to 1.2 billion metric tons, of beef to 450,000 tons and of pork to 502,000 tons.
Russia's economics ministry earlier warned that it would review the meat quotas for the U.S. if WTO talks in October fail.