Tencent Holdings Ltd. is nearing a deal to buy the Finnish maker of the popular “Clash of Clans” game in a deal that values the company at more than $9 billion, said people familiar with the matter, a move that could thrust the Chinese internet giant atop the fast-growing and lucrative mobile-games industry.

Tencent is in late-stage talks with SoftBank Group Corp. to buy the Japanese telecommunications firm’s majority stake in Supercell Oy, the people familiar with the situation said. The Chinese company also is in discussions...