RSA is in talks with a consortium of Canadian insurer Intact Financial and Danish insurer Tryg about a possible takeover.
The deal, which could see the British insurer broken up, values it at about £7.2bn ($9.46bn).
RSA, famous for its More Than brand, has large operations in Canada, Ireland and Scandinavia.
After the talks were revealed, its share price rocketed 46% to close at 670p on Thursday.
If the deal goes ahead it will be the biggest takeover of a UK-listed company so far this year.
The offer from Intact Financial and Tryg would pay 685p in cash per RSA share. It also includes a previously-announced 8p per share interim dividend.
This represented about a 50% premium to RSA’s closing price on 1 October. Analysts Jefferies said the offer price represented “more than fair value”.
“The board of RSA has indicated to the consortium that it would be minded to recommend the proposal, subject to satisfactory resolution of the other terms of the possible offer, including a period of due diligence,” the UK insurer said in a statement.
RSA was formed by the merger of Sun Alliance and Royal Insurance in 1996 and provides home, motor and commercial insurance.
Under the terms of the deal, Intact and Tryg would split up RSA’s businesses with the Canadian firm keeping its Canada and UK operations.
Denmark-based Tryg would take control of RSA’s Sweden and Norway operations, while the pair would also co-own RSA’s Danish unit.
Tryg would take on the highest bill paying RSA about £4.2bn, while Intact would contribute £3bn.
The two insurers have until 3 December to make a formal offer.
RSA has a history going back more than 300 years.
Sun Alliance had its origins in Sun Fire Office, the oldest documented insurance company in the world founded in London in 1710.
Royal Insurance was established in Liverpool in 1845.
RSA has long been seen as a takeover target and came close to a sale to Switzerland’s Zurich Insurance in 2015.
The company employs 13,500 people across more than 100 countries.