The American tire distributor could be valued at more than $2.5bn, said Reuters, citing people familiar with the matter.
TPG has interviewed investment banks for roles in the IPO, which could take place later this year.
The firm could also consider an outright sale of the business in a dual track process.
The report noted that the US auto industry shows signs of recovering from and six of the top seven automakers reported year on year increases in sales in April.
TPG is also looking to exit property listings group RentPath, which operates the Apartment Guide and Rent.com websites.
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