The Reuters investigation documented at least 12 cases of prescient messages about major Indian companies being posted in WhatsApp groups limited to traders.
"We will certainly investigate the issue. It is a work in progress," Mr Tyagi, chairman of SEBI, told news agency Reuters, when asked what action the regulator was considering.
India beefed up insider trading rules in early 2015, expanding what constitutes "unpublished price-sensitive information" to include "any information" that is not "generally available" and that could have a market impact.
SEBI also set up a panel in August headed by a former federal senior bureaucrat, T K Viswanathan, to suggest measures to improve market surveillance and help prevent possible insider trading and market manipulation.
Last year, SEBI proposed a ban on sharing trading tips and stock-specific recommendations through bulk messages, emails, blogs and social media such as WhatsApp, Twitter and Facebook, unless one is registered as an investment adviser.
The regulator said the general public was lured by the tips and their investment decisions were influenced by messages that solicit investments and promise unrealistic returns.
It has also cranked up its investor awareness drive to prevent the public from falling to scams and to boost retail investment in financial markets.