The deal would be one of the largest private equity transactions so far this year after Cerberus Capital last week announced the $9.1 billion purchase of supermarket Safeway.
Gates Global is a leading producer of power transmission belts and fluid power products for the automobile and other industries.
The company garnered $2.9 billion in sales and $25 million in profits in the year ended September 28, 2013, according to a US securities filing. Last December, Gates filed papers for an initial public offering.
Gates is controlled by Canadian private equity company Onex and the Canada Pension Plan Investment Board.
The bid by Blackstone and TPG is timed ahead of a Wednesday deadline for potential buyers to make offers, the source said.