Tard Inc. is discussing improving its takeover proposal for Seven & i Holdings Co. with the goal of convincing the Japanese convenience store operator to start engaging in talks, people with knowledge of the matter said.

Japan's Seven & i said Monday that it is open to talks with Alimentation Couche-Tard if the Canadian owner of Circle K stores improves its $39 billion bid for the 7-Eleven parent.

The operator of 7-Eleven has rejected an opening offer from the owner of convenience store rival Circle K, saying its business is worth more.

Eleven, has rebuffed a buyout offer that would have been the largest foreign-led acquisition of a Japanese company.

Seven & i on Friday declined the preliminary proposal that Alimentation Couche-Tard made last month to acquire the Japanese corporate parent of the 7-Eleven convenience store chain.

Seven & i Holdings Co. rejected a $39 billion takeover proposal from Alimentation Couche-Tard Inc. as too low and fraught with regulatory risk,

Tard’s proposal is “opportunistically timed” and “grossly undervalues” the owner of the iconic convenience store chain.

An unsolicited offer from the owner of Circle K to buy the owner of 7-Eleven stores has been rejected by 7-Eleven's Japanese owner, but some observers think that might be the last word between the convenience store rivals.

The Japanese owner of convenience store chain 7-Eleven has rejected a $38bn (£29.2bn) takeover bid from a Canadian rival. In a letter addressed to the Circle K owner Alimentation Couche-Tard (ACT), Seven & i Holdings said the Canadian company's offer "grossly" undervalued the company and was.