The $18bn (£13.3bn) deal is designed to cover billions of dollars of losses incurred in Toshiba's US nuclear unit.
The Japanese firm was almost delisted this year after delaying the publication of its financial results.
It said the deal, if approved, would ensure it remained public.
Toshiba is the world's number two chipmaker and its Toshiba Memory unit accounts for about a quarter of its revenue.
Bain Capital has partnered with South Korea's SK Hynix Inc and brought in US buyers of Toshiba chips such as Apple and Dell in order to buy the division.
