However, its controlling shareholder intended to keep the company independent.
The maker of Heineken and Amstel beers said it consulted with its majority shareholder and concluded that SABMiller's proposal was "non-actionable".
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"The Heineken family has informed SABMiller, Heineken and Heineken Holding of its intention to preserve the heritage and identity of Heineken as an independent company," it said in a statement.
The founding family owns just over 50 per cent of Heineken via Heineken Holding HEIO.AS. A further 12.5 per cent is owned by Mexico's FEMSA FMSAUBD.MX.
Citing people with knowledge of the matter, Bloomberg news agency reported SABMiller's approach earlier on Sunday, saying it was part of an SAB strategy to protect itself from a potential takeover bid from its larger rival, world No. 1 brewer Anheuser-Busch InBev ABI.BR.
Speculation about an AB InBev move on SABMiller has been circulating for months, as the world leader - known for its aggressive merger strategy - has largely digested its last acquisition. Talk of such a deal had intensified in the past week, according to sources who spoke on condition of anonymity.
[DATA SAB:SAB] was not immediately available for comment after Heineken's announcement, but declined to comment earlier in the day.
Bloomberg reported from its sources that SABMiller's offer would have made the Heineken family one of the largest shareholders in the combined group. The newswire also said that the approach was made in the past two weeks.
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SABMiller has done many deals on its journey from a small South African player to the world's No 2 brewery, including the 2005 purchase of Colombia's Bavaria, the 2007 purchase of Grolsch, the 2008 combination of Miller Brewing Co with the U.S. business of Molson Coors TAP.N and the 2011 purchase of Foster’s Group.
Like other brewers, SABMiller is struggling to grow in Europe and North America. New revenues from emerging middle classes in developing markets have been dented by weak currencies in many of those countries.
Heineken, the largest player in the mature Western European market, has expanded steadily in faster-growing emerging markets, including Mexico and Asia.