Chelsea players Azpilicueta and Christensen's contracts at Stamford Bridge expire at the end of the season. Players can negotiate transfers with other clubs in this winter window for the summer.
Full-back Azpilicueta is now 32 and Christensen is now 25. Both players are likely to leave Stamford Bridge on free this summer.
According to Spanish media reports, Barcelona are currently in talks with full-back Azpilicueta, and Barca will offer Chelsea full-backs a contract to sign until 2024.
Azpilicueta has not yet told Chelsea whether he will join Barca at the end of the season.
Azpilicueta is a Chelsea veteran. He came to Stamford Bridge from Ligue 1 from Marseille in the summer of 2012 and has made 456 appearances for the Blues, helping Chelsea win two Premier League titles, one Champions League and two Europa League and other trophies.
Barcelona are also interested in Christensen, whose contract is about to expire. The player is also in the spotlight of Bayern Munich.
Danish player Christensen is a Chelsea-trained player who has made 148 appearances for Chelsea.
Chelsea boss Tuchel wants Christensen to stay at Stamford Bridge.
Tuchel said: "He told us he loved Chelsea, he told us he wanted to stay and be an important part because he was an important part of a big club and I think he was a good fit.