Both companies' boards have reportedly agreed to a deal, said to be worth 232 UK pence ($4.24) per HBOS share, and that more details would be released on Thursday.
A takeover would mark another dramatic change in the global financial landscape as troubled firms have been bought out by larger firms or bailed out by governments.
In Russia, the authorities suspended stock and bond trading for the second consecutive day as shares nosedived on Wednesday.
On Tuesday the RTS exchange suffered its biggest single-day drop, down by 17 per cent, while the MICEX slid by 17.45 per cent despite a one-hour suspension of both markets.
Following the worst drop in 10 years Russia's finance ministry quickly promised $60bn for local banks in an effort to shore up confidence.
AIG's bailout brings to about $900bn the total of US rescue efforts to stabilise the financial system and housing market.
Edward Liddy, AIG's newly-appointed head, was said to be about to hold a huge sale of the company's assets in order to pay off a $85bn loan from the US Federal Reserve which helped save its business.
AIG, which has businesses ranging from life insurance to airplane leasing in 130 countries, is currently paying more than 11.4 per cent interest on the loan.
In London, shares in HBOS had experienced wild swings during morning trading, climbing as high as $3.94 and falling as low as $1.58.
The FTSE 100 London stock exchange closed down 113.2 points at 4,912.4 having reached a low of 4,903.3 and a high of 5,124.4 in a volatile day of trading.
Barclays, another British bank, had given Wall Street a small boost on Tuesday by agreeing to buy the investment arm of Lehman Brothers, the US bank which went bankrupt on Monday, for $1.75bn and taking on its 10,000 staff.
Barclays stock rose 10 per cent on Wednesday but major European stock indices fell after Wall Street's slide following its opening.
In Ireland, the Bank of Ireland became the latest bank to cut its share dividend payment, causing a sell-off in Irish banking shares.
Earlier in Hong Kong stocks fell 3.63 per cent to close at their lowest levels for 23 months after worries that more financial institutions could get into trouble.
AIG had faced a cash crunch after $18bn of losses over three financial quarters, largely because of complex securities that are tied to mortgages and which plunged in value as the US subprime mortgage crisis deepened.
Investors and credit rating agencies had grown more doubtful that AIG could offset its losses with enough capital, which became more costly to raise as the firm's share price plunged.
The US central bank stepped in on Tuesday amid worries that a collapse of AIG could cause far-reaching damage to the global financial system.
Reacting to the news, Daniel Fuss, a bond manager who oversees more than $100bn at Loomis, Sayles & Co in Boston, said: "Thank God. AIG is interwoven with so many people and touches many companies around the world. This is a huge relief to many parts of the financial markets."