Mark Carney has travelled to Europe seeking closer Canada-EU ties on defence, trade and business, and people.
He will visit France and will attend the State of the EU address.
According to sources, he has suggested making Canada an associated partner of the European Union.
Carney stated visa rules and a possibility of visa-free travel are included in the talks.
Some commentators note the EU's favourable view of Carney does not guarantee more straightforward trade agreements.
They also say stronger links could carry costs for Canada.