TEL AVIV—Two of Israeli Prime Minister Benjamin Netanyahu’s most formidable opponents are in talks to form a united front, and face a deadline this week to declare whether they will join their political camps to try to unseat him.

Mr. Netanyahu’s rivals from the center, Benny Gantz, a retired Israeli army chief who entered politics late last year, and Yair Lapid, a former television anchor turned parliamentarian, are under pressure from opponents of the right-wing Mr. Netanyahu to combine forces.