Serbian Prime Minister Aleksandar Vucic has signaled he could propose changes to the country's constitution that would include stripping out a reference to Kosovo as a Serbian province and could help its bid for European Union membership.

While the current government has always maintained its opposition to recognizing Kosovo’s 2008 independence, the move could make it much easier for a future Serbian administration to do so. Mr. Vucic’s comments, made in an interview with The Wall Street Journal, come at a time when EU-brokered...