The 32-year-old defender will be out of contract in the summer and so far there is no agreement between the club and the player over a new deal.
Talks have not progressed between Chelsea and the Spaniard and Barcelona are prepared to snap him up on a free transfer next summer.
Xavi Hernandez admires his former Spain team-mate and wants to add him to his Barcelona squad at the end of the season.
But it has been claimed that Azpilicueta is prioritising staying at Chelsea and signing a new contract with the club.
The Spaniard has spent close to a decade at Chelsea and his family feel settled in London.
He would prefer to continue at Chelsea but it has been claimed that he wants some sort of security from Chelsea.
The Blues have a policy of offering only one-year deals to players over 30 but Azpilicueta wants a longer deal.
The Spaniard is keen to continue at Chelsea but wants the club to do more to make him stay.
