It took about nine months for Toyo to form a special committee to assess YFO's offer, which YFO said acted against shareholders' interest.
At an annual meeting in June, Toyo shareholders approved seven of nine directors backed by YFO, allowing these directors to form a majority of the board.
It had been possible for YFO to hold talks with Toyo since the board reshuffle, the source said.
YFO had already notified Toyo of its proposal and believes it could start a tender offer by late December, the source said.
Expectations for a sweetened offer from YFO have in recent weeks boosted Toyo shares, which closed at 1,241 yen on Monday.
Yamauchi, Toyo, YFO, YFO's, Makiko Yamazaki, Alexander Smith
Japan's Toyo, Toyo, YFO, Thomson