Dairy Crest, Britain's biggest dairy firm, said "discussions are ongoing and there can be no certainty that this will result in a transaction".
Shares in Dairy Crest soared to record levels on the back of the announcement, and stood at 583p at midday Tuesday. The move may help to increase Dairy Crest's earnings by moving out of the lower value private label sector.
Dairy Crest saw strong growth from branded and added value products over the last financial year, ended 31 March. Cathedral City recently confirmed its position as Britons' favourite cheddar brand, increasing sales by 17 per cent in value and 11 per cent.
The group recently rolled out a new advert campaign for its Country Life butter, and has continued to push its St Ivel omega-3 milk. It has also bought up the doorstep milk delivery business of rival Arla Foods UK, making it the largest 'milkman' in the UK.
This deal, together with a focus on brands, suggests Dairy Crest has been looking to scale down involvement in private label dairy products for supermarkets.
The group increased sales by more than £100m to £1.4bn last year, although profits tumbled amid rising costs and a 17 per cent drop in milk sales to retailers. It predicted in May that commodity markets would remain challenging, but that branded product lines would continue to grow.