India's Ministry of Electronics and Information Technology has introduced draft legislation for such apps that run on user-generated content, and which have more than 5 million users in India, according to the FT.
Those proposed new rules will require the owners of such apps to establish a local office in the country, and appoint a senior official to be accountable for any legal concerns that might arise, the Financial Times report said.
If the law is passed, app owners will have to put in place "automated tools ... for proactively identifying and removing or disabling public access to unlawful information or content," according to the report.
Chinese apps such as video apps TikTok, Like and Helo have rapidly gained market share in India, with more of them taking over the top 10 most popular apps in the country's Android app store last year than in 2017, the report said.
CNBC contacted TikTok, Like, Helo and India's Ministry of Electronics and Information Technology for comments, but they did not immediately respond.