A group including Apple Inc. and Dell Technologies Inc. surged to the front of a hotly contested race to acquire Toshiba Corp. ’s memory-chip business, a crucial supplier to some of the world’s biggest makers of electronic gear.

Toshiba said Wednesday it had signed a nonbinding agreement with the leader of the group, private-equity firm Bain Capital, and intends to reach a deal by the end of September. The bid values the business at about $19 billion, according to people familiar with the matter.

The development is the latest twist in a global auction that has pitted three major bidders against each other and exposed a rift between Toshiba and a key partner, Western Digital Corp., which is also vying for the business. At stake is control over a key building block in everything from smartphones to heavy-duty computing machines.

Toshiba is racing to strike a deal in the wake of huge losses at its U.S. nuclear unit, Westinghouse Electric Co., which filed for bankruptcy earlier this year. The Tokyo company has said it needs to sell the profitable memory unit to bring its shareholder equity back into positive territory by the end of its fiscal year in March 2018. Otherwise, its shares would face delisting under Tokyo Stock Exchange rules.

Besides Apple and Dell, the Bain group includes disk-drive maker Seagate Technology PLC and others, and more tech and financial players may join, according to people familiar with the matter. It also includes South Korean chip maker SK Hynix Inc., as well as Innovation Network Corp. of Japan, a fund backed by the Japanese government, and government-owned Development Bank of Japan, other people said.