Philadelphia 76ers owner Harold Katz said yesterday he has agreed to sell his 58 percent stake in Nutri/System Inc. to an investor group led by senior Nutri/System management.

The investor group plans to acquire Katz's stake and all other outstanding shares of the operator of weight-loss centers with cash provided by Merrill Lynch Capital Markets, banks and currently available Nutri/System funds. The group is offering Nutri/System shareholders $59.6 million in cash, or $6.13 a share, plus debt, which the company declined to value specifically yesterday.

Nutri/System, once a soaring stock that traded as high as 48 1/8, closed yesterday at 5 5/8. In its lastest fiscal year that ended June 30, the company had revenue of $101.8 million and net income of $1.4 million (15 cents a share) versus revenue of $126.3 million and a loss of $17.5 million ($1.80) the prior year.

As of Sept. 30, Nutri/System, which is based in Jenkintown, Pa., owned 136 weight-loss centers and was affiliated with an additional 544 franchised centers in the United States and Canada. Nutri/System, which once derived significant profits from the sale of supplies to its franchisees, has not had the same profit opportunity since its franchisees sued for the right to buy diet food from other sources. In June 1984, Nutri/System settled the antitrust suit by agreeing to cut the price of food supplies it sells to franchisees.

The management group that plans to buy the company is led by Nutri/System President A. Donald McCulloch. Nutri/System said that a special committee of outside directors has determined that the buyout offer is fair to shareholders.