Sky News reported on Saturday that Allianz is one of a small number of potential buyers that have been in discussions with advisers to the AA about a possible transaction.
Private equity firm EQT is also understood to be among the parties interested in acquiring the company, highlighting the growing appetite for the British roadside assistance business.
The AA, founded in 1905 by a group of motoring enthusiasts, has become one of Britain's best-known motoring brands, with its distinctive yellow recovery vehicles a familiar sight on the country's roads.
The company was previously owned by private equity investors before being floated on the London Stock Exchange in 2014 at 250 pence a share.
Its current private equity owners have been pursuing what is known as a dual-track process for much of the year, according to Sky News. The strategy keeps open two possible outcomes: a sale of the business to a new owner or a return to the public markets through a listing on the London Stock Exchange.
The potential £5 billion valuation would make any transaction a significant deal for Britain's financial and motoring sectors, while attracting interest from both strategic and private equity investors.
Allianz and the AA declined to comment on the reported takeover discussions.
Interest in a potential sale of the company is not new. The Financial Times reported last year that the AA was targeting a valuation of about £5 billion and had begun seeking potential buyers.
For Allianz, a takeover would represent an expansion into a well-established consumer services business with a long-standing presence in the UK. For the AA's owners, meanwhile, the competing options of a strategic sale and public listing could provide flexibility in determining the next phase of the company's ownership.
The outcome of the process will depend on whether potential buyers are willing to meet the valuation being sought by the AA's owners and on the terms of any eventual offer.
For now, the company remains at the centre of a closely watched sale process, with Allianz and EQT among the names linked to what could become one of Britain's notable corporate transactions in the roadside assistance sector.