New York-based outfit Clayton, Dubilier & Rice, which bought BCA in February 2010, is on the verge of appointing half a dozen investment banks to bring the auctioneer to market later this year.
A listing could value the business at up to £1.2bn, putting it on course for the FTSE 250.
A successful listing would give CD&R a hat-trick of London floats in 2014, after the sale of shares in B&M Retail and Exova Group earlier this year raised £1.1bn and £220m respectively.
Both companies have been applauded for escaping the fate of newly listed stocks by staying above their issue price, with B&M six per cent higher and Exova up 13 per cent at the end of trading on Friday.
CD&R bought BCA for about £450m four years ago from rival private equity house Montagu Private Equity and parachuted in senior partner Fred Kindle as chairman after taking control of the firm.
A listing of the company is likely to include the search for a new chairman although it is not known if City headhunters have been appointed to find a candidate yet.
BCA is the biggest car auction market in Europe and helps flog 12,000 cars a week.
The 60-year old firm was founded by the late motor entrepreneur David Wickens, who helped turnaround Lotus Cars and sell it to General Motors in the late 1980s.
The group could join the growing stampede looking to list shares in London after the traditional lull in August, which includes shoe designer Jimmy Choo and sofa chain DFS.
CD&R declined to comment while BCA could not be reached for comment.