The WTA tournament in Montreal, scheduled for 7-16 August, is in jeopardy after Quebec Province officials requested that all sporting and cultural events be cancelled through 31 August.
The measure is aimed at slowing the spread of coronavirus.
"Tennis Canada is currently evaluating the consequences of this announcement by discussing the various options with the WTA regarding the postponement of the Rogers Cup presented by National Bank event in Montreal," Tennis Canada said in a statement.
With lockdowns and stay-at-home orders in place around the globe, tennis is at a standstill until at least 13 July.
French Open organisers postponed Roland Garros until September and Wimbledon was cancelled altogether.
"We understand the decision coming from the Government of Quebec who has to consider the health and safety of the Quebec population," tournament director Eugene Lapierre said.
"Our priority in the management of this crisis has always been to ensure the safety and wellbeing of our players, fans, volunteers, partners and employees and therefore our decisions will reflect this.
"We hope that our discussions with the WTA will allow us to make an official announcement on the status of the Rogers Cup by (Saturday)."