"We're actually trying to sign the most comprehensive trade agreement that Canada has ever signed... And we're not there," Harper's communications director, Andrew McDougall, told a media briefing.
"We're down to a few outstanding issues..., negotiations are ongoing and I don't expect that we'll be in a position to sign a deal next week."
Harper is scheduled to fly to London on June 11-13, then to Paris on June 13-15 and Dublin on June 15-17 to promote trade and investment, and underscore the importance of concluding a deal between Canada and the 27-nation European Union.
A transatlantic deal would give Canadian companies access to 500 million European consumers and eliminate 98 per cent of Canadian tariffs on EU goods.
Negotiations started in 2009 with the expectation they would be concluded by late 2012, but they became deadlocked over a few holdout issues, mainly in agriculture.