The all-cash offer represents a premium of about 50% to SABMiller's closing share price of £29.34 on September 14.
ABI is determined to get its hands on its rival to grab more of the global beer market, where it believes growth will come from acquisitions rather than selling more beer.
But questions remain about whether regulators would allow the deal, given the combined group is thought likely to make up about half the profits of the global beer industry.
AJ Bell investment director Russ Mould said: "A tie-up between the two groups would create the world’s biggest brewer, but not before severe scrutiny by anti-trust regulators, particularly in the US."
Michael Hewson, chief market analyst at CMC Markets, said: "While we now have a tentative agreement and a deal extension to October 28 with a £3bn break clause, payable by AB InBev if the deal doesn’t proceed, the combined company will still have to overcome a host of regulatory obstacles which is likely to prompt a number of disposals in China and the US."
The Belgian brewer of Stella Artois made the revised approach to SABMiller's board on Monday.
The group did it privately in the hope of persuading SABMiller to take part in talks, Britain's Sky News cited people close to the situation as saying, as it was under time pressure to act before a so-called 'put-up-or-shut-up deadline' this Wednesday.
SABMiller had already turned down a £42.15 approach and two previous proposals on the grounds that they undervalued the company.
ABI also makes Budweiser and Corona, while Britain-based SABMiller - which holds second position - owns Peroni, Grolsch and Pilsner Urquell beers.
ABI employs about 1,000 people at its UK breweries in Magor, Samlesbury and Mortlake, as well as its company headquarters in Luton. It has at least 200 beer brands.
SABMiller has around 69,000 staff in more than 80 countries, from Australia, Zambia and Colombia to the Czech Republic, South Africa and the US, also producing more than 200 beers.
Formerly known as South African Breweries, SAB acquired US rival Miller Brewing Company in 2002, resulting in the renaming of the group as SABMiller.
A merged group would be worth about £177bn and would add AB InBev's dominance of Latin America to SABMiller's strong presence in Africa, as well as their breweries in Asia.