The leading Nikkei business daily said Sony was looking to sell the division to Japan Industrial Partners for between 40 billion yen and 50 billion yen ($396 million to $495 million).
The fund would set up a new company that will continue selling PCs and laptops under the Vaio brand, in which Sony would retain a small stake, the Nikkei and other local media reported.
Sony had just a 1.9 percent share of the global PC market in the first nine months of last year, according to the Nikkei.
A Sony spokesman said the reports were "not based on anything we have announced so we decline to comment on them, but we are studying various options for our PC business".
Sony shares rose 3.33 percent to 1,581 yen in Tokyo Wednesday morning, rebounding slightly from heavy losses the previous day.
The reports come after public broadcaster NHK said at the weekend that Sony was in talks with Chinese computer giant Lenovo to set up a joint venture for its overseas PC business.
(Also see: Lenovo declines to comment on Sony Vaio PC joint venture reports)
That report added that Sony was doing a separate deal for its domestic business with an investment fund at home. Sony, which reports its latest financial results on Thursday, has called the NHK report "inaccurate".
Last week, Moody's cut its credit rating on Sony to junk, saying the once-dominant firm had more work to do in repairing its battered balance sheet.
Japan's embattled electronics industry, including Sony rivals Panasonic and Sharp, has been undergoing painful restructuring to stem years of huge losses, largely tied to the low-margin TV business.
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