Morgan can return to school for his final season if he withdraws by the May 30 deadline.
Purdue All-American Caleb Swanigan was also selected and is the highest pick of a Purdue player since 1994.
The junior guard will forego a final year of college eligibility for a chance to be a pick in the NBA Draft Lottery later this year.
Former team CEO Donnie Walsh returns to take over as team president with Kevin Pritchard being promoted to general manager.
Indiana has been chosen the number-one team in the nation for the upcoming season in several preseason polls.