Budweiser maker Anheuser-Busch InBev said it was now in exclusive talks with Asahi, which is known for its Super Dry beer, although it is yet to officially accept the offer.
The deal includes Peroni and Grolsch in the UK and Europe, as well as London's Meantime brewery, which are being put up for sale by AB InBev to help ease regulatory concerns over its £71bn takeover of SABMiller.
Carlos Brito, chief executive of AB InBev, said: "We are pleased to have received this binding offer from Asahi on the Peroni, Grolsch and Meantime brands and businesses - iconic beer brands with long-standing heritage and leading positions in core markets."
SABMiller's chief executive Alan Clark said: "SABMiller has grown Peroni and Grolsch into world-renowned premium brands, and we are confident that, along with fast-growing modern craft brewer Meantime, they will continue to thrive and develop."
AB InBev is launching a consultation with staff over the potential sale, although it is dependent on the completion of the SABMiller takeover.
Buying Peroni and Grolsch would allow Asahi to tap into growth outside a declining Japanese lager market, where it has a 38% share.
Asahi said it had been looking to grow internationally "for some time".
"Through this proposed acquisition, Asahi aims to expand its growth platform in Europe and become a global player with a distinct position," it said.
The offer includes the Peroni, Grolsch and Meantime brands, as well as SABMiller's Italian, Dutch and British operations that make and distribute the brands.
It also includes the global rights to the Grolsch, Peroni and Meantime brands, except in the United States.
AB InBev confirmed it was putting Peroni, Grolsch and its Meantime brewery on the sale block in December, less than a month after formally agreeing the SABMiller takeover following protracted talks.
It is seeking to get the green light from authorities for the deal, which marks the largest takeover of a UK-based firm as well as the fourth biggest in global corporate history.
AB InBev has already announced the sale of SABMiller's US joint venture, with partner Molson Coors agreeing to buy the remaining 58% stake in MillerCoors for 12 billion US dollars (£7.9 billion).
Its takeover of SABMiller is expected to go through in the second half of the year, if it gets clearance from regulators and shareholders.
SAB has invested heavily in Peroni in recent years, marketing the brand across Europe and America to help cement the lager as a global brand, alongside Grolsch.
A sale of the Meantime brewery in Greenwich will bring to a close a brief spell under SAB's ownership after it was bought by the group in May.
SAB, which was founded in South Africa, snapped it up under plans to tap into the burgeoning UK craft beer market.
Meantime was founded 15 years ago by brewer Alastair Hook and its most popular brews include London Lager, London Pale Ale and London Porter.