However, 10-20% of key products would continue to be protected by the current level of tariffs, including some textiles, cars, beef, lamb and dairy.
The government said it would make an announcement once a decision had been finalised.
Tariffs are taxes on imports which protect UK companies from overseas competition.
Many supporters of Brexit argue that tariffs on food and other items should be scrapped in order to lower prices for consumers.
But farmers fear that cheap imports and lower standards would destroy many parts of British agriculture. Similar concerns have been expressed in other sectors of the economy, and many business leaders fear the government could be tempted to cut tariffs at their expense.
The plans for widespread cuts in tariffs were first reported by Sky News, which said the government intended to publish details of the tariff cuts if lawmakers rejected Prime Minister Theresa May’s Brexit deal in a vote due next week.
The Department for International Trade said that no final decision had been taken on tariffs, but there had been discussion across government about the right level in the even of a no-deal.
“If we leave the European Union without an agreement, our tariffs will need to strike a balance between protecting consumers and businesses from possible price rises and avoiding the exposure of sensitive industries to competition.”
Appearing before the International Trade Select Committee on 6 February, Liam Fox said he was carefully considering all the options for tariffs in the event of no deal.
“Unilateral liberalisation [reducing tariffs to zero] is not what I would propose, and I have not heard anyone else in government propose it,” he said.
“Throughout, there needs to be a balance between the impact on consumers and the impact on producers. The government are very clear that they need to give protection where necessary, but without becoming protectionist.”
And last month, Environment Secretary Michael Gove promised farmers that the government would apply tariffs to food imports in the event of a no-deal Brexit, to provide “specific and robust protections” for farmers.
“Your concerns have absolutely been heard,” Mr Gove told a conference of the National Farmers’ Union (NFU). “It will not be the case that we will have zero-rate tariffs on food products.
“There will be protections for sensitive sections of agriculture and food production.”