Burnett handles the Beck's account in the US through its Chicago office, and was requested to take on the UK business. M&C Saatchi loses the brief.
However, Burnett and S&N are attempting to reach an agreement that may enable the agency to handle both briefs. Burnett stands to lose the Woodpecker, Bulmer Traditional Cider and Strongbow brands, should an agreement not be reached.
Bruce Haines, Leo Burnett's chief executive, said: "We have greatly enjoyed working on the Strongbow account, but we understand that both InBev and S&N need and deserve a conflict-free arrangement with their agency. We are currently discussing alternatives with S&N."
Phil Rumbol, the marketing director of InBev UK, added: "Working with Leo Burnett in the UK brings us into line with the global relationship we have with the agency."
Haines claimed that InBev had "ambitious plans" and was going to increase its spend on Beck's.
Should the resignation go through, S&N could hand the accounts to M&C Saatchi or TBWA\London, its two main roster agencies.
In May, InBev bought the right to license and distribute Beck's in the UK from S&N for £77 million. The sum will be paid in agreed annual rates until 2012.