The retailer has written to Home Secretary Theresa May, saying it would support a change in the law and a £25,000 fine for those selling drinks below cost.
It says the measure could either be included in the Police Reform and Social Responsibility Bill or taken forward in a Private Members Bill.
Director of corporate affairs Richard Taylor said: “As a leading British retailer we recognise the dilemma that exists over the sale of discounted alcohol for government and the industry.
“Having considered the arguments thoroughly, Morrisons believes that the best way for the government to intervene is to introduce a compulsory ban on off-licence sales of alcoholic beverages below the rate of duty and VAT.”
There is widespread support in principle across the industry for a ban on below-cost drinks sales. Loss-leading takes place primarily on lager, and occasionally Champagne and spirits, but is not as common in the wine category.
But there is a debate about how cost should be defined. The WSTA, like Morrisons, believes it should simply reflect duty and VAT, but trade bodies including the Federation of Wholesale Distributors and the British Beer & Pub Association argue it should also include some of the production costs – though not necessarily the full invoice price paid by the retailer.