The company, which runs a chain of rehabilitation clinics, best known for treating pop stars such as Robbie Williams, is understood to be close to appointing investment banks to run the float after asking them to come forward and pitch for the mandate.
Its owners, the private equity firm Advent International, is said to be already working with the company’s independent financial adviser Rothschild on the prospective deal.
The flotation is expected take place in the first half of next year and could value the company at as much as £1bn, according to reports.
Advent and Priory declined to comment.
Advent bought Priory in 2011 from the Royal Bank of Scotland for £925m. The company has around 300 facilities across the UK, treating about 30,000 patients for mental health disorders, ranging from anorexia and depression to gambling and drug addiction.
Group revenue in the year to the end of December rose by 8.3 per cent to £520.7m, up from £480.8m the previous year. Adjusted earnings rose by 2.6 per cent to £129.7m, while pre-tax losses halved from £72.4m to £35m.
In December, the group opened a clinic in the City, designed for a growing number of workers suffering from stress and depression.
Priory joins a number of companies planning a London float, including pharmaceutical firms Therapeutics and Finnish Faron Pharmaceuticals. Payments processing firm Worldpay, which is also part owned by Advent, is also weighing up a potential listing or trade sale.