The new bid, at $18.19 per share, was more than 20% higher than ACT's previous offer for the Japanese company and was sent last month, Bloomberg said, citing people with knowledge of the matter.
Seven & i said it was not in a position to comment as it was determining the facts of the report. Canada's ACT was not immediately available for comment.
The Japanese company's shares pared their gains and were up 4.7% at 2,335 yen ($15.76) as of 0130 GMT.
If it were to go ahead, the deal would be the largest ever overseas buyout of a Japanese firm.
The operator of the 7-Eleven convenience store chain rejected the original offer last month saying it "grossly undervalues" its business.
Seven & i reports quarterly earnings on Thursday and analysts and investors are awaiting news on its plans to increase corporate value.
Last week sources told Reuters that it was considering selling a stake in its supermarket unit and Bloomberg reported that it was considering selling part of its Seven Bank holding.
For several years Seven & i has been under pressure from foreign investors, including ValueAct Capital and Artisan Partners, to improve its asset allocation.
