SABMiller, the world's second-largest brewer by volume, will pursue Foster's after its A$9.5bn (€7bn) cash offer was rejected by Australia's biggest beer company.
The maker of Peroni said that it will "continue to seek engagement" with Foster's, which last month spun off its wine unit to focus on beer.
Foster's rose 14pc in Sydney. SABMiller offered A$4.90 a share, or 8.2pc more than Monday's closing price.
The bid may spark a takeover battle for Melbourne-based Foster's. Japan's Asahi Breweries and Mexico's Grupo Modelo are among rivals that may make offers, according to analysts.
SABMiller may have to raise its bid by about 13pc, based on the price paid by Kirin Holdings in 2009 for Lion Nathan, Australia's second-largest brewer, said Dirk Van Vlaanderen, an analyst at Jefferies International in London.
"We expect SABMiller to return with a higher bid," said Andy Bowley, an analyst at Citigroup.
"SABMiller remains the most likely acquirer of Foster's."
SABMiller shares fell 3.6pc in London. The gain in Foster's shares was the steepest in more than 25 years.
Including debt, the bid is worth A$11.2bn, SABMiller said. The offer values Foster's at 11.8 times the A$948m in earnings before interest, taxes, depreciation and amortisation that the company's beer division posted last year.
Kirin said it paid 13.8 times Ebitda for the 54pc of Lion Nathan it didn't already own in 2009.
"We suspect the Kirin/Lion multiple will represent the board's benchmark for a accepting a revised or alternative bid," Citigroup's Bowley said.
That would equate to a range of A$5.40 to A$5.50 a share, or 10pc to 12pc above the rejected bid.
"There's room to go higher if you compare them to some recent deals," said Will Seddon, at White Funds Management in Sydney.
"There have been a whole lot of transactions in that space in recent years, many of which were done at pretty high multiples."
Heineken and Carlsberg paid 23 times EBITDA for the UK's Scottish & Newcastle in 2008.
A takeover of Foster's by SABMiller would be the biggest acquisition of a brewer since InBev NV acquired Anheuser-Busch for $52bn in 2008.
Modelo, the maker of Corona beer, is also interested in Foster's, it was claimed earlier this month. The Mexican company discussed with its board a proposal to make a joint bid for Foster's with Molson Coors, it was reported.
SABMiller chief executive Graham Mackay said he had no information on possible counter-bidders. A spokeswoman for AB InBev declined to comment on whether the world's largest brewer would bid for Foster's.
Heineken said it doesn't comment on competitors' acquisition plans.
SABMiller, which submitted its proposal to Fosters' chairman yesterday, said it had given no indication that it would move to a hostile bid.
An acquisition of Foster's would be SABMiller's biggest, giving the maker of Grolsch about 50pc of Australia's beer market, including the top-selling Victoria Bitter. ( Bloomberg)