The combined value of the two firms is likely to be at least $230bn (Â£150bn) based on Tuesday's share price.
AB InBev's brands include Budweiser, Stella Artois and Corona, while SABMiller owns Peroni and Grolsch.
If the deal is successful, the merged company would produce one third of the world's beer.
AB InBev said it had approached SABMiller's board about a "combination of the two companies".
However, it added that there was no certainty the approach would lead to an offer or an agreement.
Earlier, SABMiller said it had been informed that AB InBev was planning to make a bid, but that it had no details as yet.
"No proposal has yet been received and the board of SABMiller has no further details about the terms of any such proposal," the firm said.
Shares in SABMiller jumped more than 20% on the news, while AB InBev's shares were 11% higher.
"Let's get this straight, this is a takeover by AB InBev of SABMiller. It's not a merger," said Larry Nelson, editor of the industry trade magazine, Brewer's Guardian.
Given the size of the deal both parties would be likely to have to sell off parts of their operations to get it past the regulators, and that may mean sacrificing some of their US and Chinese businesses .
"In the US SABMiller has a joint venture with Molson Coors which gives it a 25% share of the market and makes it a clear number two," Mr Nelson added.
"But combining with the number one, AB INBev, would give them 75% of the market, which is clearly untenable. But AB InBev would not have gone into this without having some plan of what they want to divest."
The merged company would be likely to move aggressively into faster growing markets.
AB InBev has an eye on the South African markets where SAB Miller dominates in 15 countries, and has a presence in a further 21.
A merger would also strengthen its grip on South America and Mexico which are by far its most profitable markets.
This deal has long been anticipated but analysts believe AB InBev was held back from making an offer because of high levels of debt built up through a string of other purchases.
SABMiller has also been trying to do deals. Last year it made an unsuccessful offer for its smaller rival Heineken in a move that was widely seen as an attempt to ward off a bid from AB InBev.
The prospect of a tie-up between the world's two largest brewers is looming after Anheuser-Busch InBev said it had made a takeover move for SABMiller.