The Chinese government is pushing some of its biggest tech companies—including Tencent, Weibo and a unit of Alibaba—to offer the state a stake in them and a direct role in corporate decisions.

Wary of the increasing power of private businesses, internet regulators have discussed taking 1% stakes with social-media powers Tencent Holdings Ltd. and Weibo Corp. and with Youku Tudou, a YouTube-like video platform owned by e-commerce titan Alibaba Group Holding Ltd., according to people close to the companies.

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