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.
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.