The two firms are among a number of interested parties in the private healthcare operator.
The talks follow a strategic review by Spire Healthcare announced on 18 September 2025 and remain at a preliminary stage.
Bridgepoint and Triton are required to make an offer for the business by 21 February 2026.
Sky News reported the deal is believed to be around £1.5bn and to have been prompted by shareholders' concern about a fall in the company's share price.
Spire Healthcare, which is the UK's largest private healthcare operator in revenue terms, has 38 hospitals and over 50 clinics, medical centres and consulting rooms.
The FTSE 250 company was founded with the acquisition and re-branding of 25 Bupa hospitals in 2007.
Spire, which is a strategic supplier to the NHS, works in partnership with over 8,740 experienced consultants to deliver care to over 1.3m patients.
It acquired Thames Valley physiotherapist Physiolistic Ltd for an initial fee of £5.2m in July 2025.
The company reported a 9% rise in NHS revenue in March 2025 while warning of a £30m hit to earnings in the year ahead driven by a rise in National Insurance and Minimum Wage costs.
