Sainsbury's and Morrisons are already competing with strong campaigns on fresh food provenance.
According to Kantar, Morrisons' advertising showed good results, with a 7.3% year-on-year uplift in sales of fresh and chilled goods despite the supermarket's overall market share slipping from 12.1% to 12%.
There was an opportunity for organic to bounce back following increased demand for premium fresh food, said the company, but organic must be linked to superior product quality.
Premium products, particularly own-label, are important across all categories at the moment as retailers look to deliver a 'premium Christmas'. The focus is set to stay on premium in the New Year, with particular emphasis on fresh foods.
"Fresh is still a real point of difference for supermarkets. With Morrisons, for example, shoppers increasingly cite the fresh fixture as a reason to shop there," said Kantar's Ed Garner.
"The mood has shifted and people are talking about food rather than price. That presents an interesting challenge for those in the middle. We're likely to see things like free-range, Fairtrade, sustainability and local become more important."
Garner warned against relying on the organic label alone to deliver sales. "The top four organic brands are doing well because they are quality products, not just because they are organic."
Garner first presented the Kantar findings at The Chartered Institute of Marketing’s Food, Drink & Agriculture event.