CBI sources said the meeting took place on the sidelines of a function in Mumbai when the minister visited there on April 16.
Within a fortnight of this meeting in which two more persons were understood to be present, they said, Kumar assumed charge of Member (Staff) in the Railway Board.
The sources said Kumar is changing his version about the meeting and evasive in his responses.
They said although such meetings are part of protocol as senior officials of a railway zone meet the minister whenever he is on tour, but in the present context of serious bribery allegations even such seemingly innocuous meetings need attention.
The probe agency wants to get a clear picture whether it (the meeting) had to do with Kumar's posting or a routine one, the sources said.
The CBI has arrested eight persons in connection with the bribery scandal which allegedly involves Bansal's nephew Vijay Singla and Kumar. Singla was arrested for receiving Rs. 90 lakh part payment of "bribe amount" allegedly routed by Kumar through middlemen.
The sources said the money was part of the Rs. 10 crore promised for lateral shifting of Kumar from Member (Staff) to Member (Electrical), which is considered a lucrative posting.