Sport says the Spanish giants are so keen to sign the duo that they have already sent representatives over to London to get the deals done.
Reports suggest that they have already convinced Azpilicueta, 32, to make the switch when his contract expires in June.
He will be offered a two-year deal with the option to extend for a further season.
Xavi is said to be a big fan of the Chelsea captain and is eager to get the deal over the line.
Barcelona are also planning to make a move for Christensen, whose contract also expires in the summer.
He has attracted interest from other clubs across Europe, including Bayern Munich.