American International Group Inc
The reports could not immediately be confirmed.
One source with knowledge of the issue said it was not yet certain whether there would be a media briefing later in the day.
If confirmed, the deal would draw to an end a more than year-long saga fraught with delays and political wrangling that saw an earlier deal rejected by regulators, forcing AIG to wait for the cash it needs to repay its U.S. government bailout.
Ruentex has long been seen as the front runner, but any deal would still be subject to regulatory clearance.
Sources have told Reuters that Ruentex, a major player in the hypermarket business in China and Taiwan, may not meet all of the five strict criteria the regulator has laid down for a buyer.
Two Ruentex units, Ruentex Development Co Ltd <9945.TW> and Ruentex Industries Ltd <2915.TW>, have teamed up with Pou Chen Corp <9904.TW>, a maker of Nike Inc
Ruentex Development shares were up 4.3 percent on Wednesday, while Ruentex Industries and Pou Chen rose 6.3 percent and 3.1 percent, respectively.
Nan Shan is Taiwan's No. 3 insurer by market share after the insurance arms of Cathay Financial Holding Co Ltd <2882.TW> and Fubon Financial Holdingg Co Ltd <2881.TW>. It has about 4 million policyholders - about one-sixth of Taiwan's population.
Nan Shan has assets of T$1.7 trillion ($56.5 billion) and lost T$12.7 billion in the second quarter of last year and T$12.5 billion in the third quarter.
(Reporting by Taipei bureau; Editing by Chris Lewis)