Broadcom offered about 2.5 trillion yen ($23 billion) for Toshiba's chip unit, the highest among 10 or so bidders who participated in the first round of offers, a source briefed on the matter said.
Taiwan's Foxconn made the second highest offer, of about 2 trillion yen, the source said, declining to be identified as he was not authorised to speak on the matter publicly.
Broadcom and Foxconn were among four suitors selected to proceed to the second round, several sources said, adding that Broadcom has partnered with US private equity firm Silver Lake Partners LP.
South Korea's SK Hynix and Toshiba's chip joint venture partner Western Digital Corp are the other suitors, but Western Digital's offer was far lower than those of Broadcom and Foxconn, the source said.
The size of SK Hynix's offer was not immediately known.
Toshiba has said it needs to sell most or all of the prized business to cover charges related to U.S. nuclear unit Westinghouse Electric that threaten the Japanese conglomerate's future.
Representatives for Broadcom, Silver Lake, Foxconn and Western Digital could not be reached immediately for comment outside of regular business hours. A Toshiba spokeswoman declined to comment on the specifics of the sale process.