Brightside has emerged a surprise contender to take over RAC as part of a consortium.
Insurance Times understands the AIM-listed company has been in talks with banks and private equity houses about putting together a bid for the firm, although discussions have been at early stages.
Any deal is likely to involve bank and/or private equity investment, with Brightside taking over the management of the business.
Brightside declined to comment. One possibility could be for Brightside to team up RAC with personal injury law firm New Law.
Helen Molyneux founded New Law in 2004 and she is also a non-executive director with Brightside.
Brightside is an attractive option for private equity because it has a solid insurance background and could help maximise the potential of RAC's insurance arm.
There is a unanimous feeling among investors that the insurance arm of RAC has underperformed and there is still large scope for improving its performance.
The battle to buy RAC is highly competitive and five private equity firms are understood to be in the hunt.
One of the private equity firms is Clayton Dubilier & Rice which would run the business alongside BCA Europe, the European second-hand car dealer it bought last year.
Another bidder is understood to be private equity firm Carlyle, which like Clayton Dubilier & Rice owns a stake in car rental firm Hertz.
Analysts believe RAC would sell for around £600m. Aviva called in advisors JP Morgan to handle the sale process in March.