"Conversations are well advanced but until everything is signed it is best to wait," Barcelona sports director Txiki Begeristain told Spanish magazine AS on Thursday.
"We are very optimistic and confident we can settle the operation before Monday."
Juventus are in the middle of a complete exodus from team stars after the club were found guilty in the Italian football match fixing scandal and thus were relegated to Serie B plus a 30 points deduction.
Barcelona was first to approach Juventus for the pair, and Thuram expressed his delight on the prospect of joining the UEFA Champions League champions.
"I am very excited, but I feel at this stage I cannot say too much as I still have to speak to Juventus," Thuram told El Mundo Deportivo sports paper.
Spanish media suggest that Barcelona will be paying around 19 million Euros to capture Zambrotta, while 24-year-old Thuram is due to join the club on an initial one-year-contract.