Are there legal concerns if the the hospital where I have priveleges offers professional discounts to physicians?

Yes, there are legal concerns. The anti-kickback statute prohibits an entity from giving something of value, such as discounts on services in this case, to induce referrals.

Employed physicians and physicians who are independent staff make referrals. If a hospital discounts its services to the physicians, it could be seen as an inducement to refer.