The 22-year-old right-back has been linked with a switch to the Blues for some time and Marseille recently admitted their main aim this summer was to reduce the wage bill.
Azpilicueta is one of the players they would be prepared to sell for the right price, and reports suggest he is now close to completing a £7million move.
Having progressed quickly since he joined Marseille from Osasuna in 2010, Azpilicueta understandably feels a sense of loyalty to the French club.
However, he recognises that a sale would ease their money worries and is open to the idea of going to Chelsea.
"Everyone thinks it's been a tough time with my thoughts split between Marseille and Chelsea," Azpilicueta said in the Daily Mirror.
"But if my departure can help Marseille's finances, it's good for everyone."