The pitch, which is being handled by The Haystack Group, is expected to kick off next week.
A review has been on the cards since Andrew Harrison, the former Nestle marketing chief, took over as the managing director of Muller Dairy earlier this year.
Muller appointed Publicis in August 1999 following a pitch against Rainey Kelly Campbell Roalfe/Y&R and Bates. Its previous agency was Saatchi & Saatchi.
However, the Publicis chief executive, Grant Duncan, claimed he was not aware of any pitch. "We have not been informed of a pitch; we have had nothing in writing," Duncan said.
Publicis created the Muller Love brand campaign, which included sponsorship of the TV show Blind Date. TV executions for the company included a spot for its Mullerlight brand, which featured a young couple plotting to join the "Mile High Club". A second execution is currently on air, showing the boyfriend naked and locked out of his hotel room.
In May this year, the agency created a TV campaign for its probiotic drink Muller Vitality. In April, Muller overhauled the packaging of the range to take on the leading brands Actimel and Yakult.
Tim Lindsay, the chairman of the Publicis UK Group, said that the agency is continuing to develop work for the brand and hoped to hold on to the account. "If we're not successful, then we'd expect them to look elsewhere," he said.
Separately, Muller is reported to be reviewing its pan-European media account. In the UK, this is held by ZenithOptimedia.
The media review is being conducted from the Muller headquarters in Germany.
It follows the appointment of Jens Oliver Hauck, who joined as the European marketing director from Procter & Gamble.
Zenith was first appointed to the media account in 1995 following a shootout against Vizeum, then called BBJ.
Muller Dairy (UK) is a subsidiary of Molkerei Alois Muller GmbH, a privately-owned company based in Germany. Its range of products consists of more than 70 yoghurts and desserts, which can be split into three categories: healthy yoghurt, desserts and children's and drinks.
Harrison was unavailable for comment at the time of writing.