Toshiba has put part or all of its valuable memory chip unit up for sale to plug a gaping hole in its finances.
Foxconn's potential bid is much higher than analysts' $18bn valuation for the business, Bloomberg and the Wall Street Journal reported.
At least one other firm has also submitted a preliminary bid, they said.
Such a large offer from Foxconn would put pressure on Japan's government as Toshiba is seen as a key national asset.
The Japanese firm needs to raise funds after its US nuclear unit, Westinghouse, filed for bankruptcy protection last month.
Toshiba has warned that its net loss for 2016 could exceed 1 trillion yen ($9bn; £7bn) - one of the biggest losses in Japanese corporate history.
Toshiba is the world's second-largest chip manufacturer, with its products used in data centres and consumer goods worldwide, including iPhones and iPads.
It would not be the first bid for a Japanese firm from Foxconn, which assembles most of Apple's iPhones.
Last year Foxconn struck a $3.5bn deal to take a majority stake in Sharp, the struggling Japanese electronics company.
South Korea's SK Hynix and US chipmaker Broadcom have also submitted preliminary bids for Toshiba's chip business, according to Bloomberg.
Taiwan manufacturer Foxconn has signalled it could mount a $27bn (£21.7bn) bid for Toshiba's chip business, according to reports.