A spokesperson for May said the Prime Minister wants to "tackle corporate irresponsibility and reform capitalism to make sure it works for everyone not just the privileged few".
Read more: Seven numbers explaining the demise of BHS
May's comments come after a joint inquiry by the work and pensions select committee and the business, innovation and skills select committee found that Green's family became "incredibly wealthy" during their 15-year ownership of BHS, leaving the retailer and its pension fund weakened to the point of collapse.
However, the inquiry also pointed to failures in corporate governance.
Shadow business, energy and industrial strategy minister Jon Trickett said what had happened at BHS was partly down to "individual greed" but was also "a failure of weak corporate governance structures".
He urged the government to launch a review of how such companies are governed and how their professional advisers operate, according to the BBC.
The Institute of Director's head of corporate governance, Oliver Parry, said: "The business community will be very worried about the damage this episode will do to public faith in capitalism. Now is the time to take a fresh look at how large private-owned companies are governed. Just because a company is not listed on the stock market it does not mean there is no public interest in how it is run.
"After damning reports into BHS, and last week Sports Direct, there is a pressing need to work out how to raise levels of trust in how British companies are overseen."