The company previously said that the three members would nominate a candidate to replace Ghosn, who was arrested last month for alleged financial misconduct.
The source, who declined to be identified as the matter was confidential, said a nominee would be chosen from within the existing board as early as Tuesday, and submitted to the rest of the board at their next meeting on Dec 17.
Nissan officials were not immediately available for comment.
The three independent board members are former bureaucrat Masakazu Toyoda, racing car driver Keiko Ihara and retired Renault executive Jean-Baptiste Duzan.
Ghosn's detention has left the Renault-Nissan-Mitsubishi auto alliance without its leader and main interlocutor with the French government, which owns 15 percent of Renault and wants to maintain the ownership structure enshrining its control of the partnership.
(Reporting by Maki Shiraki; Writing by Ritsuko Ando; Editing by Keith WeirEditing by Keith Weir)