Apple and Dell are among the firms involved in the consortium, said Foxconn chief executive Terry Gou.
Foxconn, the world's biggest contract electronics manufacturer, makes the iPhone for Apple.
Mr Gou said Amazon could also come on board, while talks continued with Google owner Alphabet, Microsoft and Cisco Systems.
Apple declined to comment, while others did not respond to requests for comment.
It was not clear say how much Foxconn planned to offer for the division, which analysts have valued at about $18bn (Â£14.2bn).
Earlier this year it was reported that Foxconn could offer as much as $27bn for the unit. It was not clear why the potential bid was so much higher than its mooted value.
Toshiba is selling some or all of its chip unit to cover huge losses in its nuclear division, Westinghouse Electric, which has filed for bankruptcy.
It was the latest headache for the Japanese conglomerate. In 2015, Toshiba's chief executive resigned after the firm said it had overstated profits for years. It is also set to post another annual loss.
Toshiba: What's going wrong?
Toshiba shareholders angry as chip unit sale approved
The memory chip unit is said has attracted interest from several firms including Western Digital, Micron Technology, SK Digital and Broadcom.
Previously, it was reported that Foxconn would offer $27bn. Foxconn acquired Japan-based Sharp last year.
Toshiba hopes to announce a deal by mid-June, with shareholders voting on the sale on 28 June.
The Japanese government plans to examine the national security considerations of a deal. That could present a challenge to Taiwan-based Foxconn, which does much of its manufacturing in China.
Foxconn has lined up several high-profile US technology firms to join its bid for Toshiba's memory chip unit.