The European Champions are aiming to firm up their interest with Marseille willing to listen to offers of over £8 million for the 22 year old Spanish right back.
Azpilicueta would be Roberto Di Matteo's fourth summer signing as the Italian looks to add depth and quality to his Champions League winning side.
And Spanish star Azpilicueta appears to be the next name on the list, with Marseille reportedly willing to listen to offers of over £8 million.
The French club's chairman, Vincent Labrune, is quoted in The Sun as saying: "Chelsea have made a serious approach for Cesar [Apilicueta]."
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Chelsea are short on options in the position after allowing Jose Bosingwa to leave the club on a free contract, with Paulo Ferreira the Blues' only out and out right back and Branislav Ivanovic a utility option.
The 22-year-old Spaniard started his career at Osasuna before moving to the South of France in 2010, helping Marseille to the French League Cup 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.