Apparatus for preparing and dispensing hot or cold milk, in the frothed or non-frothed state, in a coffee machine for preparing various types of beverages based on coffee with milk, said coffee machine comprising a coffee apparatus for producing coffee with an associated coffee dispensing device, a first water heater for producing steam, a second water heater for producing hot water for preparation of the coffee in said coffee apparatus, said first and second heaters being connected to a water source for replenishing them with water, a frothing device provided with an internal chamber for frothing the milk when required and at least one nozzle for dispensing the milk externally, said apparatus comprising a milk line for the milk, connecting a source of liquid milk to the frothing device, a steam line for the steam, connecting the first water heater to the frothing device, as well as an air line for the air, connecting a source of air to the said frothing device, a pump arranged along the milk line for supplying the milk from said source of liquid milk to said frothing device, a first intercept valve arranged along the steam line and a second intercept valve arranged along the air line, wherein said pump arranged along the milk line and said first and second intercept valves are able to be operated independently of each other such that the milk line, the steam line and the air line are connected to said chamber of the frothing device one at a time or in combination with each other.