A private equity firm has reportedly made a bid to own some of the UK’s best-known insurance brands which are being sold by the Royal Bank of Scotland.

The UK’s Mail on Sunday has reported that private equity group CVC Capital Partners recently made a £4 billion ($6.2 billion) offer for Royal Bank of Scotland Insurance (RBSI).

RBSI, which owns brands such as Direct Line, Churchill and Privilege as well as affinity specialist UKI and commercial insurer NIG, recently flagged that it was open to a trade sale ahead of a slated float of the business at the end of next year.

The bank’s latest report shows the insurance division’s performance is improving, with a third-quarter profit of £123 million ($189 million) compared with a £33 million ($51 million) loss in the corresponding period last year.

Premium income was £1.04 billion ($1.6 billion) and net claims £734 million ($1.1 billion). RBS says net premium has fallen due to the run-off in non-core areas, de-risking of the motor insurance book and the exit from unprofitable business lines.

CVC already has an interest in the insurance industry with a 50% stake in Brit Insurance, and tried to buy a majority stake in RBSI in 2008 in a joint venture with Swiss Re.

The Mail on Sunday quoted sources close to RBSI as saying it had received other expressions of interest for the business in recent months, with Berkshire Hathaway, Zurich and Generali listed as potential suitors.

The RBSI business is currently valued at £4.3 billion ($6.7 billion), and the bank must divest a majority stake in the insurance arm by the end of 2013 under a competition ruling by the European Commission.

The European decision followed the state bailout of the bank, which is now majority-owned by the UK Government, during the 2008 global financial crisis.