Boston-based Bain was previously said to be on the verge of buying TI for almost $2bn (£1.3bn) in November 2013. However, this transaction fell apart after the US firm reportedly dropped its offer to $1.5bn. And in 2011, Bain was one of three private equity firms to make an offer to TI.
The manufacturing firm makes fuel tanks and braking and power-generating components for cars and trucks. While it is currently headquartered in the US, it was founded in Birmingham.
TI is now controlled by asset management firm Oaktree Capital and it supplies companies such as Mercedes-Benz, Audi and Honda.
Both Bain and TI declined to comment yesterday.