Multiple sources tell The Canadian Press the two sides recently settled on a quota that is big enough to allow Canadian meat producers to penetrate the European market, but not so big that European farmers would feel threatened.
No one is talking publicly for fear the deal could unravel, falling victim to the horse-trading that characterizes the final rounds of trade negotiations.
"It seems like they have found a place to agree," said one person close to the talks who spoke on condition of anonymity.
But since the beef and pork conundrum was a potential deal-breaker for Canada, insiders are growing optimistic that the elusive agreement may now be within reach.
On Thursday, International Trade Minister Ed Fast was in the heart of cattle country, boasting about the market access the Canadian government had negotiated for the beef industry. He went out on a limb, saying only a few barriers remain in the trade talks.
"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.
"As with all trade negotiations, the toughest issues get left until the very last."
Fast's spokesman Adam Taylor wouldn't confirm whether a specific breakthrough had been made on beef and pork, but did say Canada has been pressing for greater access to the EU market.
"We have made that point very clear to our EU counterparts," Taylor said in an interview Friday.
"If that message has been received by our EU counterparts, that's good news for moving the negotiation forward."
Sources say there are still several contentious areas, apparently including financial services, procurement, cheese, fish and investor state dispute settlements.
Talks have been bumped up to the highest level of government in recent months in the hopes of breaking the logjam that has held up any formal announcement of a deal.
At the same time, Ottawa insiders say Prime Minister Stephen Harper wants some economic trophies to put in the showcase for his throne speech next month. On Thursday, Finance Minister Jim Flaherty announced a new plan for what he hopes will become a national securities regulator.
Stuart Trew, a trade expert with the Council of Canadians, said his organization's executive director was dismayed to hear of a breakthrough on "agricultural issues" when he visited Brussels recently to present European parliamentarians with a petition signed by Canadians who oppose the deal.
Trew said the council is concerned that Harper will agree to a deal, under pressure to get something finished before the ramping up of Europe's talks with the United States in October. The council has repeatedly criticized the government for being too secretive about the negotiations.
"We've seen there's a lot of pressure on Harper from the business community in Canada, from Europe," Trew said in an interview Friday.
A Canadian source close to the talks, who insisted on anonymity, said inaccurate information on the talks has regularly leaked from Brussels from a variety of sources, including EU parliamentarians, member countries and various agencies.
"I would caution anyone to think that there's been a complete resolution on agriculture across the board. Negotiations continue on these matters and a variety of other matters," the source said.
"Anyone telling you that there's a big breakthrough and we're preparing to make it public is not close to the talks."
If Harper and the EU are able to agree on the broad strokes of a free trade and investment deal over the coming weeks, they are likely to present it to the public in the form of a framework, with technical details to be worked out in the following weeks before the entire deal and all its intricacies are presented.
At that point, the Canadian provinces and the EU states would still have to sign off on it.
"I do get the sense that we're getting closer," said Kathleen Sullivan, executive director of the Canadian Agri-food Trade Alliance.
While she hopes to see a deal soon, she praised Harper for his restraint, saying he has held out for a better deal instead of caving to pressure to sign on just for the sake of having something to say.
"We need to finish the deal in a way that's good for Canada," Sullivan said in an interview.
Indeed, Harper has been under growing pressure to show concrete progress, with the business community fearing Canada will lose momentum if four years of discussions are allowed to become five.
The influential Canadian Council of Chief Executives warned in an open letter to Harper last week that talks with the EU were "at a make-or-break point."
"Your recent interventions with European leaders were welcome, but we are concerned by reports that significant obstacles stand in the way of an agreement," wrote council president John Manley.
"Unless both sides move quickly to make the necessary concessions, we fear that the CETA may slip out of reach and, with it, Canada's opportunity to secure preferential access to one of the world's largest markets."
Canada was seeking two different concessions from the EU in the beef and pork area.
Because the EU insists that its beef and pork be free of growth hormones and Canada's meat is largely produced with hormones, the quota for Canadian meat has to be large enough to make it worthwhile for producers to set up hormone-free herds. Hormone-free beef is generally more expensive to produce.
Secondly, Canada wanted assurances from the EU that European governments would not set up non-tariff barriers to Canadian meat, using the back door to prevent Canadian products from competing with their own.
Agreement has been reached on both points, sources say.
"It's a breakthrough," said a different source who asked not to be named.