Men with erectile dysfunction may be able to avoid the awkwardness of a doctor’s visit by buying the drug Cialis without a prescription, under a proposal announced Wednesday by the drug’s maker, Eli Lilly, and the French pharmaceutical company Sanofi.

Under the plan, Sanofi is buying the rights to seek approval to sell Cialis over the counter in the United States, Europe, Canada and Australia after certain patents expire. Cialis is to lose its patent protection in the United States and Europe in 2017, after which sales are expected to drop sharply as cheaper generic alternatives arrive on the market.

If approved for over-the-counter use, Cialis could gain an advantage over prescription competitors like Viagra, sold by Pfizer. But it is not clear whether the Food and Drug Administration or other regulatory bodies overseas would approve such a move: In 2008, Pfizer abandoned an effort to make Viagra available without a prescription after the European Medicines Agency raised concerns.

“Millions of men worldwide trust Cialis to treat E.D.,” or erectile dysfunction, said David A. Ricks, president of Lilly Bio-Medicines, the unit of Lilly that oversees Cialis. “We are pleased to work with Sanofi to pursue a path that could allow more men who suffer from E.D. to obtain convenient access to a safe and reliable product without a prescription.”