Winning Highland Spring, which sponsors British tennis star Andy Murray, would be a coup for Coke because it is the UK's second-biggest water manufacturer after Danone, which owns the Volvic and Evian brands.
Earlier this year, Marketing had reported that Coke was considering a summer rollout of its Belgian water brand Chaudfontaine.
The reports, which have so far been neither confirmed nor denied, suggest Coke could pay as much as £500m for Highland Spring, which is based in Perthshire in Scotland.
As Britons drink ever more water and non-fizzy soft drinks, Coke is desperate to get into the UK market where it has had no success after its disastrous efforts with Dasani.
Coke was forced to pull Dasani, which has been a success in the US, after the story broke that the brand was not mineral water, but purified tap water from Sidcup that in addition contained traces of a carcinogen called bromate.
The news of talks to buy Highland Spring follow earlier reports that the US drinks firm was looking to snap up AG Barr, which makes Irn Bru and the Strathmore water brand.
For Coke, news of the deal follows its purchase last week of Glaceau, an American vitamin-added water for £2.1bn.