First, why keep a sale confidential. If employees know that a business is for sale, they may become distracted or anxious and thereby less productive, look for other jobs, leave, or try to negotiate unreasonable terms to stay.
If landlords find out too soon, they may not be as receptive to lease extensions, renewals, or modifications. If suppliers learn, they may restrict their credit terms, look for alternate customers, raise prices. If competitors become aware of the sale, they may begin to market more aggressively, tell the public to scare customers and prospects into leaving the company for sale. All this eventualities will have a negative impact on the company's sales and profits and that will have a direct negative effect on the final purchase price.
Furthermore, in most cases, a potential buyer will recognize that a non-confidential business listing will adversely impact the business, make it less valuable, and, therefore, they will offer a lower price.
Second, how to keep it confidential. The business needs to be advertised with professionally-written copy that provides enough information to attract interest but not so much as to reveal its identity. Then, it is always best to have a business broker acting as an intermediary to obtain a strict non-disclosure agreement (NDA) and buyer profile to assure that the offering will be kept confidential and that the buyer has the apparent ability to purchase the business.
Only after the broker has received the NDA and profile should the business details be revealed.