Plans for the cuts will, according to the paper, be laid before the supervisory board at its next meeting on December 12th.
Unions fear that the sheer numbers involved could mean some could be compulsory redundancies, and said it would resist such measures.
"If that is so, we will not cooperate," Lothar Schröder from services union Verdi, told the Handelsblatt.
T-Systems has been a concern for years, the paper said. It manages the information technology contracts for large customers such as Shell, a sector which is considered highly competitive with only slim margins.
Strategies for the future include turning more to digital areas of operation such as cloud services, where T-Systems boss Reinhard Clemens hopes profits will be greater.
The outsourcing branch will retained, but other areas will be completely closed down, with several foreign subsidiaries being eyed for the axe. The Handelsblatt said the firm was considering abandoning its Spanish business and that the subsidiary in France would have to become significantly smaller.