Mark Carney is currently Europe seeking closer Canada-EU relations on defence, trade and business, and the movement of people.
He will visit France and will attend the State of the EU address.
Based on reports, he has put forward making Canada an associated partner of the EU.
Carney said visa regulations and a possibility of visa-free travel will be part of the talks.
Some commentators note the bloc's positive view of Carney is no guarantee of easier trade agreements.
They also say closer ties could carry consequences for Canada.