The 22-year-old, who is currently in England playing for Spain in the Olympic football tournament, is seen by Chelsea as the ideal man to replace Jose Bosingwa - who has left the club after his contract expired.
Marseille's sporting director Jose Anigo has admitted that £7million-rated Azpilicueta may be sold to raise funds for new signings.
"Everybody has to sell before buying," he told RTL. "In effect, it could either be (Stephane) M'Bia and Azpi. But for now, nothing has changed."