Canadian Prime Minister Justin Trudeau had been due to fly to Brussels for the summit.
But Wallonia leader Paul Magnette said late Wednesday that his region would not be able to approve the deal in the coming hours, making it ever more unlikely the full signing ceremony with Trudeau could be held on Thursday.
Officials have warned, however, that several more steps would be required before the deal is ready to be signed.
The way to a solution may be open on CETA (Comprehensive Economic and Trade Agreement), as Belgium could be close to reach a common position on the agreement.
European Council President Donald Tusk said earlier that the chances of the EU-Canada summit taking place on Thursday were waning.
Talks continued during the week, until Canadian Minister of International Trade Chrystia Freeland walked out of negotiations on October 21, declaring that she had chose to return to Canada, citing her belief that the European Union was "not capable of having an international agreement".
Lawrence's comments came as federal and regional Belgian politicians failed to break their deadlock over the deal on Wednesday, but agreed to resume talks on Thursday in a sign they may be nearing a consensus that would keep the deal alive.
When and if the documents are agreed by the Belgian politicians, they must be sent for review to the ambassadors of all 28 European Union member states, then likely return to the Wallon parliament and other Belgian government institutions. I believe that, after today's talks, the climate and situation regarding CETA, and perhaps future trade agreements, will change for the better, added Tusk.
Manfred Weber, head of a conservative bloc in parliament, told broadcaster Hessischer Rundfunk that it was a mistake to allow all European parliaments to vote on the trade pact.
It took five years of negotiations before the CETA was declared to be concluded on August 5, 2014, although what was described as the final text of the agreement was not released until two months later, on September 26, 2014.
The Canadian government publishes a formal notice in the Canada Gazette seeking input on the possibility of negotiating a trade agreement with the EU.
Politicians in Wallonia, which has a population of 3.6 million compared to over 500 million for the whole European Union, argue that the proposed accord would undermine labour, environment and consumer standards.
But leaders of Wallonia, a 3.5 million-strong French-speaking region south of Brussels, want guarantees CETA will not harm local interests.