Lawmakers and conservative advocates who fought to make it easier for Americans to use experimental medicines are floating a new twist: permitting drugmakers to sell unapproved drugs at a profit.

The “free to choose” idea is in early stages of conversation, largely among conservatives. It would shortcut clinical trials, which are the costliest of the decade-long drug development process and can run into the billions.

The free-to-choose push seeks to build upon the Right to Try Act, which President Donald Trump signed into law last year. It allows patients with life-threatening diseases to petition a drug company for an...