The proposal is aimed at allaying the Japanese government's concerns over any transfer of sensitive technology to investors it deems a risk to national security, it said.
Foxconn may also team up with Apple Inc for the bid, the report said, following a similar report by public broadcaster NHK earlier.
Yukihito Uchida, a spokesman for Toshiba, declined to comment on Apple's involvement and the NHK article.
Taiwan's Foxconn, which manufactures most of Apple's iPhones, has reportedly indicated that it is willing to pay up to 3 trillion yen for the unit.
An investment by Apple would be its first direct stake in a major global memory chipmaker as it seeks to secure a stable supply of key components. Elpida is now owned by US -based Micron Technology Inc.
The iPhone maker is actively looking at options for helping the troubled Japanese company by investing in its semiconductor unit, which has been put up for sale, according to people familiar with the matter. Toshiba [s:jp:6502] is trying to sell its chip business to raise cash after massive cost overruns from its USA nuclear power unit, Westinghouse, which filed for bankruptcy last month.
Toshiba shares rally on rumours of much-needed cash injection by Apple.
The candidates for the Toshiba bid was recently narrowed down to four companies including SK hynix, Taiwanese firm Hon Hai Precision, also known as Foxconn, the world's third largest memory chipmaker Western Digital and American private equity firm Silver Lake Partners.
Toshiba's semi-conductor unit is now the world's second largest flash memory chip manufacturer.
"It is not true Toshiba has put the chip sale process on hold", a Toshiba spokesman said.