The World Cup in South Africa is four years away - but the country's beer has been knocked out during qualifying.
SABMiller owns Miller Lite as well as local brands like Castle
American giant Budweiser has gained the exclusive rights to sell beer inside 2010 World Cup stadiums.
Local brands met the same fate as the national side, which made an early exit from the recent Cup of Nations and failed to reach the 2006 World Cup.
SABMiller, the biggest local brewer, says it does not have a suitable brand for the $100m sponsorship deal.
"SABMiller does not have any international beer brands that sponsor football - consequently, this would not be an appropriate venture for us," head of media relations Nigel Fairbrass told the BBC News website.
Fifa says SABMiller was approached as a potential sponsor but did not respond.
"We waited for three months for them to respond, and they did not, so we signed with Budweiser," Jerome Valcke, chief executive officer of Fifa Marketing and TV, told a seminar this week.
Mr Fairbrass said he was not aware of SABMiller having been approached, but said that would not have changed the company's position with respect to the sponsorship.
SABMiller, now the world's second-largest brewer, was formed from a merger between South African Breweries and United States-based Miller.
In South Africa, it markets long-established SAB beers such as Castle and Amstel, as well as international brands such as Miller Genuine Draft and Pilsner Urquell that arrived in South Africa as a result of the merger.