The probe, which could lead to disciplinary action, is being headed by Ken Corsar, Glasgow's director of education, and concerns the handling of the contracts by two of his most senior and best known colleagues, Ian McDonald and George Gardner, and Ronnie McLellan, a service manager in the education department. The council's legal and audit teams are also involved.
It is understood that work on school software programs was allegedly handed to an Edinburgh-based computer company headed by Mr McDonald's son.
Mr McDonald is the high-profile depute director of education who steered through the council's controversial privately funded programme of secondary school modernisation, which included upgrading systems for information and communications technology. He has been on sick leave since before Christmas.
The council, as is common in staffing matters, would not comment in detail. A statement said: "There is an internal inquiry under way regarding certain tendering procedures within education services. In the event that anything amiss is uncovered, action will be taken, including disciplinary action if necessary."