LV= said it was in "exclusive discussions" regarding a potential transaction involving Bain Capital but gave few details.
Bain Capital bought esure in a cash deal worth about £1.2bn in 2018.
Bain is a US-owned private equity firm which invests around the world and has approximately £80bn in assets under management.
LV=’s board said its focus was on maximising long-term value for members and ensuring the business continues to be operated in their best interests, following the disposal of the general insurance business.
The company added that discussions between LV= and Bain Capital were "on-going" and there was no certainty that any transaction will be agreed.
The two organisations will make further announcements "if and when appropriate."
Speculation has been swirling around LV= recently that it would agree a merger or takeover deal with a third party, with Royal London reported to be in the fray. Royal London has declined to comment on a potential tie-up.
LV=, which was also subject to takeover speculation in June, said that it was continuing to trade well despite the impact of Covid-19.
LV= recently sold off its its general insurance business and has been looking at a number of options for the firm’s future.
In January LV= appointed former Zurich senior executive Mark Hartigan as chief executive on an initial 12 month contract. Mark Hartigan was part of the senior leadership team at Zurich Insurance Group.
At the beginning of 2020 LV= became a company limited by guarantee, ending its friendly society status.
LV= has approximately 1.25m member customers who own ‘a member-qualifying product’ - this includes current and historic products, apart from equity release products and customers who have general insurance products. Overall the company has 5.5m customers and 3,500 employees.
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