According to business news website The Currency, Exponent is in exclusive talks to acquire the group for around £300m.
It reported in October last year that business advisory firm PwC had been appointed to sell the group, which is based on Lisburn Road in south Belfast.
A spokesperson for PwC said it could not provide any comment or detail on the process.
Exponent did not respond for a request for comment, while a spokesperson for Kingsbridge also did not respond.
It would be another major deal on the island of Ireland for Exponent, after it acquired Chanelle Pharma in the Republic. It was founded by the father-in-law of jockey Sir AP McCoy.
According to The Currency, Kingsbridge attracted strong interest from both private equity and other operators in healthcare during the process.
Kingsbridge Healthcare Group operates four private hospitals, including one on the Lisburn Road and one in the Republic.
The company posted turnover of £105.6m in the year to March 2023, according to latest accounts filed at Companies House. Pre-tax profits were recorded at £11.4m, up from £9.1m.
There are also entities registered in the Republic of Ireland, including Kingsbridge Private Hospital Sligo Limited.
In August last year, the group opened a £2.25m surgical facility with complementary eyecare services at its hospital in Ballykelly.
Anthony McKenna, general manager at Kingsbridge Private Hospital North West, said: “This new centre of excellence has been established to meet the needs of patients in the North West who previously had to travel greater distances to access treatment for cataracts or plastic surgery.”
Aside from its presence on the Lisburn Road in Belfast the group also has a base at the newly redeveloped Kings Hall Health and Wellbeing Park.
Suresh Tharma, founder and director of the group, was interviewed by Insider Media last month. He described how the business had been sent up in 2005 with a focus on supporting the NHS with managing waiting lists.
However, in 2015 its NHS work dropped dramatically, leading to cost-cutting and redundancies. It then switched to a private-only model.
Mr Tharma told Insider Media: “Given the lack of a long-term waiting list plan in the NHS recently it’s very difficult to project forward with NHS work with any confidence and to plan ahead.
“We therefore can only build to full capacity when we know a facility will be filled. And the only way we could do this was by focusing on private patients and we’ve reaped the benefits from this strategy.”