Famed hedge-fund manager David Tepper plans to turn Appaloosa LP into a family office managing his personal wealth as he spends more time focused on running the Carolina Panthers, his professional football team, said people familiar with the matter.

Executives at the $13 billion hedge fund have discussed several scenarios for when they could return outside clients’ money, some of the people said, including over several years or around the end of this year. One of these people said a period of several years was more likely. Mr. Tepper’s money makes up more than 70% of the firm’s assets under management.

A spokesman for Appaloosa said the firm hasn’t set an exact time table for the return of all outside money. Appaloosa is among a small number of hedge funds that has regularly returned some investor money over the last decade in an effort to manage their size and returns.

Employees have been told Mr. Tepper’s investment business is changing, said people familiar with the matter, and some have been interviewing with other investment firms. Some employees have been told they are welcome to stay and make investments for the family office.

The expected change would mark the next chapter for one of Wall Street’s most widely respected investors.The son of an accountant who grew up in a middle-class Pittsburgh neighborhood, Mr. Tepper founded Appaloosa in 1993 after repeatedly being passed over for partnership at Goldman Sachs Group Inc. Appaloosa’s performance, though volatile, catapulted Mr. Tepper to a rarified level of wealth and prominence. He is known for his big bets and blunt delivery.