Elpida will submit its restructuring plan to the Tokyo district court by August 21, according to the report.
Micron has not commented on the report.
Japanese Elpida Memory filed for bankruptcy protection in February with more than 400 billion yen of liabilities.
Acquiring Elpida would double Micron?s share of the global market for DRAM. That would help the company vie with industry leader Samsung.
SK Hynix Inc. had publicly expressed interest in buying Elpida, but the company decided to drop its interest in last month.