SINGAPORE—China's government plans to issue more than a dozen licenses that would allow companies to offer after-school tutoring, according to people familiar with the matter, capping months of turbulence for a once-flourishing industry devastated by new restrictions.

Tutoring companies including Gaotu Techedu Inc., previously known as GSX Techedu Inc., and Tencent Holdings Ltd. -backed Yuanfudao, have engaged in discussions with regulators in recent weeks about an arrangement that would allow them to resume offering tutoring services to students in the ninth grade and below, said people familiar with the talks.