Francois Dumontier, promoter of the race in Montreal, told the espn.co.uk website that an extension to 2024 was on the table.
He said that was the longest agreement ever proposed to Canadian organizers, with previous deals being for five years with options.
"All new agreements now being signed are for 10 years," he added, saying that there were several reasons for that.
"I believe they want to consolidate the good grands prix. Montreal is such a race, undoubtedly. We saw as much (this year) with the full grandstands and the comments made by the drivers and teams.
"F1 has a project to enter the stock market. Ten-year contracts have a certain value when entering the stock market," he added.
Formula One supremo Bernie Ecclestone said in April that the company behind the sport could be floated in Singapore at the end of this year if markets remained benign.
Plans to raise up to $3 billion by listing the business were pulled last year amid market turmoil following the flotation of social network Facebook, whose shares plunged after their debut.
Several grands prix are nearing the end of their current contracts, with Australia's ending in 2015 along with Barcelona, while Bahrain's runs out in 2016. Singapore signed a five-year extension in 2012.
The newest race on the Formula One calendar in Austin, Texas, has a 10-year contract. Silverstone, which hosts this month's British Grand Prix, agreed a 17-year deal in 2009.
(Reporting by Alan Baldwin, editing by Mark Meadows)