Talks between the two sides have been dragging on for years with a couple of deadlines already coming and going.
Menzies said the proposal is more complex than the North American Free Trade Agreement, which took years to hammer out.
"These are complicated negotiations and it is a totally different level," Menzies said following a speech at the EU-Canada Conference in Calgary.
"It's the new style of free trade agreement and we don't even call them free trade agreements. They are economic and trade agreements," he said.
The wide-ranging negotiations, which would give Canadian exporters access to the world’s single largest market, have proven much more difficult than anyone expected.
Talks began in 2009 and the initial completion date was the end of 2011. That was pushed back a year and now it's anybody's guess.
"There's a lot at stake and when you hear the number values — like $17 trillion — there's a lot of interest at stake here so it's very important and we need to get it right."
A member of the European Union delegation to Canada told the audience that they shouldn't be concerned about the delays or problems with the ongoing negotiations.
Maurizio Cellini, head of the economic and trade section for the EU delegation, said they've made progress during nine rounds of negotiations over three years.
He said the talks have reached a very advanced state.
"We truly hope to be able to overcome the remaining obstacles in the coming weeks and we hope to be able to close the negotiations quite soon."
Menzies declined to discuss what the sticking points are, but said it doesn't involve contentious issues such as the fuel quality directive, a proposal that would penalize fuel derived from Alberta'a oilsands.
"That won't be a topic for discussion in the negotiations," he said.