A potential buyer is India's Tata Consultancy Services, the people said.
Postbank Systems has around 1,400 employees, mainly in the German city of Bonn. A sale would help Deutsche reach its goal of shedding 18,000 staff overall to cut costs and restore profitability.
Bloomberg News first reported the development.
Deutsche Bank and TCS declined to comment.
(Reporting by Tom Sims and Patricia Uhlig in Frankfurt and Sankalp Phartiyal in New Delhi; editing by Thomas Seythal and Maria Sheahan)