The agency has yet to be formally appointed but is the only one left in the running, following a pitch against the Toronto-based incumbent, The Hive, and Vallance Carruthers Coleman Priest.
Charlie Hiscocks, SAB Miller's brand communications director, oversaw the review.
Once it has been put into research and finalised, Mother's work will provide overall brand positioning while re-launching the US premium packaged lager in a selection of countries.
The work is scheduled to run in various markets around the world, including the UK. However, it will not be used in the brand's main market and country of origin, the US.
Miller Genuine Draft has not advertised in the UK since March last year, when it ran a campaign created by Rainey Kelly Campbell Roalfe/Y&R.
The agency parted company with the brewer after it was appointed to the global account for Carlsberg.
Mother's New York office, which opened last year, was awarded the creative advertising account for SAB Miller's Milwaukee Best back in May. Previously, the brand had not advertised since its 1997 "release the beast" ad.