Mark Carney is currently Europe seeking closer Canada-EU links on national security, trade and economic ties, and the movement of people.
He is heading to France and will attend the European Union State of address.
According to sources, he has put forward making Canada an associated partner of the EU.
Carney said visa requirements and potential visa-free travel will feature in the discussions.
Some commentators note the bloc's favourable view of Carney is no guarantee of easier trade negotiations.
They also say a deeper partnership could carry drawbacks for Canada.