But he cautions that doesn't mean an announcement is imminent.
"There's still a very, very small handful of issues left outstanding that need to be resolved," Fast said at a beef industry forum in Calgary Thursday.
"As with all trade negotiations, the toughest issues get left until the very last."
Negotiations on the proposed Comprehensive Economic and Trade Agreement (CETA) started four years ago.
Fast declined to say what issues remain on the table.
He said the issues would require "political decisions", and that both sides are looking for "creative ways" of bridging the remaining gaps.
Canada is seeking better access for Canadian pork and beef, drug patents and other goods.
Market access was the key topic as Fast and Agriculture Minister Gerry Ritz met with producers at Canada Beef Inc.'s annual forum.
And Canadian efforts to resolve a long-simmering dispute with the United States over country of origin labelling (COOL) was one of the main issues people attending the conference were chewing on.
Ritz said the COOL rules are so bad even the American meat industry sought an injunction to prevent its own government from putting the policy into play.
"They've identified some several hundred million dollars a year it will cost them to comply," Ritz said. "So are American consumers going to pay for that, or is it going to be reflected in the offer for our beef and hogs?"
Washington first imposed its labelling system in 2008, a move the U.S. Department of Agriculture said was designed to help consumers make informed decisions about food choices.
The labelling system cut Canadian cattle shipments to the U.S. in half within a year and cut the export of slaughter hogs by 58 per cent.
The U.S. amended its country-of-origin labelling regulations on beef and pork after the World Trade Organization ruled against Washington. But Canada believes the amendments are even worse.
As a result, Ottawa released a list of U.S. goods earlier this year that could be subject to punitive taxes if the COOL regulations aren't overhauled again.