The NIH is being pushed to remodel the way it offers taxpayer-funded intellectual property to drug companies as gene therapy and the eye-popping prices that accompany it become more prevalent.

The latest concern surrounds affordability for future gene therapy drugs made using research associated with LentiGlobin BB305—a potential cure for sickle cell disease that has received hundreds of millions of dollars in federal grants. Sickle cell disease is a blood disorder that primarily affects people of African descent.

The advocacy group Patients for Affordable Drugs estimates taxpayers invested more than $300 million into development of LentiGlobin BB305, according to a...