Mother is understood to have presented ideas for a Christmas ad as part of its work on the main Coca-Cola brand in the UK. Its "bring me sunshine" commercial is currently airing in the UK.
The win will come as a blow to Wieden & Kennedy, which was appointed as the global flagship agency for the brand in October last year after a final shoot-out against the WPP agency Sra Rushmore United.
Wieden & Kennedy has since developed a global campaign called "the Coke side of life", with a series of viral films that aim to show that Coke is "happiness in a bottle".
A spokeswoman for Coca-Cola said: "We work with a number of agencies. Wieden & Kennedy is our global agency on the 'Coke side of life' campaign, but it doesn't stop us looking at our other agencies if their work is right for the brief."
Last Christmas, Coca-Cola aired a global campaign created by McCann Erickson Madrid, which featured a punk version of the song White Christmas.
This replaced the long-running campaign featuring a family of polar bears supping Coca-Cola.
Mother declined to comment on the win.