Bupa's £500m bid for Westminster Healthcare may be referred to the Competition Commission, as was the group's aborted takeover of Community Hospitals Group (CHG).
The Office of Fair Trading (OFT) can refer cases where the bid is for more than £70m or where the combined company would have more than a 25% share of the market.
An OFT spokesman said: “This bid may well be one that qualifies.”
He said cases can be referred “when a bid is announced or when there is a bidding contemplation”.
Westminster Healthcare, which owns the Priory Clinics favoured by troubled celebrities, is owned by Whitehall, a private equity fund controlled by Goldman Sachs and Welsh, Carson, Anderson and Stowe of New York.
As well as the 29 Priory Clinics, Westminster runs 6,000 premium care beds, where patients pay for their own care.
Other bidders for Westminster are thought to include Capio, the Swedish healthcare group which eventually acquired CHG, and BC Partners, owners of Britain's largest private hospital group General Healthcare.
If Westminster is sold off, its senior management, which set up the company two and a half years ago, would become millionaires. Westminster's chief executive Chai Patel owns 10% of the company.
Neither Bupa or Westminster Healthcare would comment on the bid.