Negotiations are ongoing and the two sides are said to be very close to reaching a deal. Pressure is mounting on negotiators to wrap it up, particularly because the United States is expected to announce the launch of its own negotiations with Europe and Canada wants its deal done.
Sources have told CBC News that the federal government is considering making the unusual move of announcing an "agreement in principle" as a backup plan if the deal isn't signed by mid-June.
Harper leaves Tuesday for London, then he will make stops in Paris and Dublin before going on to the G8 summit in Northern Ireland beginning June 17. Harper will have bilateral meetings with the country's leaders and will be underscoring the importance of completing the trade deal, according to his director of communications, Andrew MacDougall.
Those wondering if Harper will sign the Comprehensive Economic and Trade Agreement (CETA) while in Europe got their answer on Friday when MacDougall briefed reporters about the trip. "We're not there yet. We're down to a few outstanding issues. I won't speculate or comment on what they are but negotiations are ongoing and I don't expect that we'll be in a position to sign a deal next week," MacDougall said.
"But that said, we're at the negotiating table pressing hard and we'll continue to negotiate hard in Canada's interest," he said.
The European beef market and changes to intellectual property regulations around pharmaceuticals are reported to be some of the outstanding issues. The negotiations have been dragging on for years. CETA was supposed to be done in 2011, then 2012, and now mid-way through 2013 it is yet to be signed and new talks between Europe and the U.S. could be getting underway.
NDP Leader Tom Mulcair said his party is worried about how the Conservatives are handling the deal.
"We're quite concerned that in the current context the desperation of the prime minister leads him to sign a bad deal. Desperation is a singularly bad adviser," he said at a news conference in Ottawa.
Mulcair also took the opportunity to state his party's position on CETA. The Conservatives often say the NDP is anti-trade.
"This is an important trade deal. It's the future of our economy that's involved when you're dealing with a partner of that size in Europe. We want everyone to understand the NDP is in favour of dealing with Europe in this type of deal," he said, adding that Europe has good labour and environmental standards that put it and Canada on a level playing field.
Government says Canada will sign deal only when ready
NDP trade critic Don Davies said the Conservatives have allowed a previous trade surplus to plummet and that their approach to trade deals has been "extreme and ideological."
"The Conservatives' failure to properly manage the trade file is hurting the Canadian economy," he said.
Davies said he wants to see a deal that creates real market access for Canadian exporters in services, manufacturing and agriculture and he asked whether the Conservatives will protect Canada's supply management system or not. The NDP promised to pay close attention to the details of the deal, once it's finally signed, to make sure it is a balanced deal that is in Canada's interest.
MacDougall said the government won't be signing any deal that isn't in Canada's interest.
"The primary consideration has to be, is the deal good for Canada?" he said. "And that's the deal we’ll sign.
"When we're ready and satisfied with the deal we have on the table we'll sign it."
International Trade Minister Ed Fast repeated that position in question period Friday when asked by Davies what sacrifices Canada is going to be making in the deal.
"It is pretty rich for the New Democrats to get up in this House and claim to be the great born-again free traders of the world. Theirs is the party that sends its leader abroad into the United States to bash our resource industry and to badmouth our economy," said Fast. "The New Democrats have no credibility on trade. They are anti-trade, anti-investment."
Fast said the Canada-EU trade deal is expected to add $12 billion to Canada's GDP and at least 80,000 jobs.
MacDougall said Harper will be promoting trade and investment on his trip and also discussing international security issues such as Syria, Iran and North Korea. He will address the British parliament while in London and also meet with Queen Elizabeth.