Presentations are expected to take place by the end of September, with either a shortlist or a decision expected by mid-October.
India is Unilever's second-largest Asia Pacific market. Only China and Japan are bigger.
The review is statutory. One industry source said: "It's a huge piece of business and, to be honest, it's difficult to pick another agency that can compete with MindShare."
Unilever is expected to complete a review of its South Korea media business by next month, and to extend it to Taiwan by the end of the year.