Russia's Deputy Economic Development Minister, Alexei Likhachev, told journalists in Moscow last week that the agreement with New Zealand was "very likely" to be signed this year, the Interfax news agency reported.
The New Zealand spokesman said "all partners" were committed to a high quality and comprehensive agreement.
"As is to be expected, the key outstanding issues in the negotiations relate to market access for New Zealand's agricultural exports into the customs union," he said.
New Zealand's exports to Russia grew 351 per cent from $51 million in 2000 to reach $230.4 million in 2012, which included $106 million worth of dairy products, $55 million of meat and $20 million of fish.
Kiwi exports to Belarus and Kazakhstan are much smaller - worth $635,588 and $1.6 million, respectively, in 2012.
Average tariffs on New Zealand goods entering Russia range from 5.45 per cent on electrical machinery to 9 per cent on dairy products, fruit and vegetables.
While New Zealand's exports to Russia are small compared with those shipped to major trading partners such as China, Australia and the United States, ExportNZ executive director Catherine Beard said thatthe prospects for growth werestrong.
"An FTA would be very much welcomed by New Zealand exporters," Beard said, adding that it was important the agreement provided comprehensive access for this country's agricultural exports.
When the FTA negotiations were announced, former Fonterra chief executive Andrew Ferrier said the dairy co-op was thrilled by the prospects the agreement offered.
He said Fonterra exported mostly butter and cheese to Russia, faced tariffs ranging from 5 to 15 per cent and exported $120 million worth of product to that country in 2009.
New Zealand is also negotiating FTAs with India and South Korea, as well as the Trans Pacific Partnership (TPP), a trade and economic negotiation covering 12 countries including the United States, Japan, Canada and Mexico.
Exports to Russia
Total: $230.4m in 2012
Dairy: $106m
Meat: $55m
Fish: $20m