The owner of David Lloyd Leisure is in talks about a £2bn takeover of BCA Marketplace, the owner of WeBuyAnyCar.com.
BCA released a statement confirming "advanced" discussions on a 243p-a-share offer with TDR Capital after a report by Sky News .
The proposed deal will also include a 7p-a-share dividend, making the offer worth 250p a share, or about £2bn.
BCA said its board would unanimously recommend acceptance of any such firm offer.
A deal would provide some relief to the embattled fund manager Neil Woodford, whose firm Woodford Investment Management has become the subject of parliamentary and regulatory scrutiny over his decision to block investor withdrawals from his flagship fund.
Woodford is a big investor in BCA but will have forfeited a chunk of his potential windfall from the sale of his shares to TDR by reducing his stake in the company in recent weeks.
The discussions about a takeover of the FTSE-250 company come a year after an approach to BCA from Apax Partners ended without a deal being agreed.
BCA - which is better known as British Car Auctions - is involved in a spectrum of automotive services, including vehicle exchange and finance.
It also operates the largest transporter fleet in the UK, and provides vehicle management services to a range of corporate clients.
Its expansion has been driven by an aggressive push into new overseas markets which has established it as Europe's largest vehicle reseller.
The company's vehicle-buying division operates in Europe under the name CarTrade2B.
BCA is run by Avril Palmer-Baunack, its executive chairman, who previously held top jobs at Stobart Group, the infrastructure conglomerate.
She also ran Autologic Holdings, the logistics group.
BCA floated in the spring of 2015 through a reverse takeover by Haversham Holdings priced at 150p a share.
The company's shares have slipped by more than 10% during the last 12 months, sparking renewed interest from private equity firms and frustrating executives who believe the shares to have been mispriced by public investors.
A 250p-a-share deal would come at a roughly 30% premium to Wednesday's closing share price.
BCA is due to announce annual results next week.