New Chelsea owner Todd Boehly arrived in Barcelona from London on Thursday to meet with the Spanish club's directors and discuss the departures of Azpilicueta and Marcos Alonso, two of Barcelona's targets in the transfer window.
The meeting comes before the English side leave on a tour of Asia this Saturday, as all parties want a solution to the situation before they depart.
Negotiations have been delayed considerably by the change of ownership at Chelsea.
The departure of Roman Abramovich and many of his executives have left something of a power vacuum that has led to an impasse in the operations that Barcelona already had underway.
The Catalan giants have had an agreement with both players for some time.
Other Chelsea targets
A number of other players could be included in the talks between the two clubs.
There are rumours about the possibility of Frenkie de Jong, although the Dutchman's plan is to go to Manchester United, where Ten Hag has been pushing for his arrival.
However, the Blues intend to explore the option, as well as that of Dest and other players.