The decision is part of an evaluation of the business, which Carlyle bought a majority stake in for around £300m in April 2013.
The evaluation, to be conducted by Credit Suisse and likely to be completed by autumn this year, will look into whether Carlyle should sell the minicab business, or if the private equity firm should look to invest further in Addison Lee. Investment could potentially expand the business, both to other UK cities and internationally.
Addison Lee was founded by John Griffin in 1975, starting in Battersea with a single car, but expanded to over 4,500 minicabs in service today.
The firm transports over 10m passengers a year in London.
It also runs a courier service with over 1m deliveries a year.
The news of the potential sale follows increasing competition in London between black taxi cabs and private-hire minicab firms in a crowded market, with smartphone apps being offered by Hailo and Uber recently adding to the mix.
Tensions hit a peak earlier this month over Uber in particular, as black cab drivers took to Trafalgar Square in their thousands to protest against the San Francisco-founded company, on a day that included protests in other European cities such as Paris, Madrid and Berlin.
Addison Lee was itself hit by protests at its offices in 2012, following comments by founder John Griffin in the company magazine. He suggested that cyclist deaths in the capital were an unavoidable result of increased numbers of untrained cyclists using London roads.
Addison Lee has continued to make gains in recent years, as revenues increased 16 per cent to £171.6m in the year to August 2013, and net profit tripled to £16m during the period.
Carlyle Group declined to comment yesterday.