The European champions are aiming to firm up their interest, with L'OM willing to listen to offers in excess of €10 million for the 22-year-old Spanish right-back
The Spaniard would be Roberto Di Matteo's fourth summer signing, as the Italian looks to add depth and quality to his Champions League-winning side.
Azpilicueta appears to be the next name on the list, with Marseille reportedly willing to listen to offers of over £8 million.
Marseille president Vincent Labrune, is quoted in The Sun as saying: "Chelsea have made a serious approach for Cesar [Azpilicueta]."
Chelsea are short on options in the position after allowing Jose Bosingwa to leave the club on a free transfer, with Branislav Ivanovic and Paulo Ferreira currently the Blues' only senior right-backs.
The 22-year-old started his career at Osasuna before moving to the south of France in 2010, and helped Marseille to the Coupe de la Ligue in consecutive seasons.
But he has found his international opportunities limited, missing out on a Euro 2012 call-up with Real Madrid defender Alvaro Arbeloa preferred.