The Japanese convenience store operator plans to make a final decision on the sale as early as the middle of this month, the report said. It may also be considering an investment of around 20 percent in Don Quijote, the report said, without citing sources.

Shares in FamilyMart gained 5 percent and Don Quijote jumped 9.4 percent in Tokyo after the report.

A spokesman at FamilyMart said nothing had been decided, when asked about the report. A Don Quijote spokeswoman declined to comment.

Looking to expand but faced with a shortage of suitable suburban locations, Don Quijote, popularly known as "Donki" in Japan, last year took a 40 percent stake in Uny, the general merchandise store unit of FamilyMart Uny.

Don Quijote also said in August it would be interested in buying Warmart Inc's Seiyu supermarket unit.

(Reporting by Sam Nussey and Ritsuko Shimizu; Editing by Chang-Ran Kim)