The newspaper said promoter Francois Dumontier, with a new ten-year race contract with Bernie Ecclestone in his pocket, is having talks with potential investors regarding his company Octane Racing Group.
La Presse said Dumontier is open to selling "up to 50 per cent" of the company.
"I am talking to several people," Dumontier confirmed. "I think right now we have a value, and I am looking at my options as any businessman would. This is a normal process."
The Canadian grand prix is promoted by Dumontier, but Ecclestone also has separate funding agreements with various levels of government.
Dumontier, 48, reportedly had earlier talks with investors involved in New Jersey's proposed F1 race, "but the project fell through", La Presse said.
What would help Dumontier's efforts now is a new sponsor, as the Montreal race at the iconic Circuit Gilles Villeneuve has been without a title backer since 2003.
He admitted he hopes to "announce a title sponsor for 2016", as Dumontier is in "serious discussions with several partners".
"For this it takes between 12 to 15 months of discussion," he claimed, "and this year is the first time I have had enough time (for that)."
Dumontier told La Presse that about half of the grands prix on the calendar also do not currently have title sponsors.