Mark Carney is currently Europe seeking closer Canada-EU relations on military matters, trade and business, and citizens.
He travels to France and will attend the State of the EU address.
According to sources, he has proposed making Canada an associate member of the EU.
Carney stated visa regulations and a possibility of visa-free travel will be part of the negotiations.
Some commentators note the bloc's positive view of Carney does not ensure simpler trade agreements.
They also say stronger links could carry costs for Canada.