Without knowing precisely what NDIPs you are talking about nor the actual relationship between your bank and the brokerage firm - I would say YES - your regulator may very well have some concerns.
Some of the questions that immediately come to mind are: Is the use of the brokerage firm to execute the trades for the bank's portfolio or for a client account? If the proposed transactions are for the bank's portfolio, are you able to document best price and execution? If the proposed transactions are for a client account, what disclosures are you providing to the client to avoid potential conflicts of interest?
I would suggest that you consult with your legal counsel before proceeding down that road.