The advertiser is believed to be in contractual negotiations with PHD to shift the £1m UK media work without a pitch for the business.
The family-owned company has achieved a high profile across the UK due to contracts with major retailers and supermarket chains such as Tesco, Sainsbury's and Asda.
But it has strong competition from Wolf Blass, Jacobs Creek, Kumala, Blossom Hill and increasingly from supermarket own brand wines.
As well as Ernst & Julio, Gallo's brands include Sierra Valley, Turning Leaf, Sanoma Selection, Single Valley and Estate Bottled wine.
The firm has recently tried to up its profile by placing advertising in the Guardian Weekend magazine and Observer Food Monthly.
The wine sector has seen several brands try to shift their public perception. Perceived downmarket wines Mateus, Blue Nun and Black Tower have all gone through redesigns to take themselves towards the brand perceptions of labels such as Ernst & Julio Gallo.
Carat confirmed that the advertiser was due to move from the agency.