The government "is now working on the adoption of a consensual Brexit," said Michael Gove.
Mr Gove said his team was still seeking an agreement with Brussels, but wrote in the Sunday Times: "No deal is a very real perspective now."
Mr. Johnson blamed Mr. Gove for planning a Brexit without a deal.
Prime Minister Boris Johnson has asked Mr Gove to chair seven days a week According to the paper, it would not be enough to change Theresa May's readmission agreement, approved by the EU but firmly rejected by Parliament, until Brexit.
- Brexit: What's next?
"You can not just warm up the returned dish and expect it to be tastier," he wrote.
He hoped that EU leaders could agree to the idea of concluding a new deal, "but we must assume that this will not be the case".
"Whi If we look to the future with optimism, we are realistic that planning is needed in all cases."
Mr. Gove pointed to a major flaw in Ms. May's deal as an Irish stoppage plan – a measure which should prevent the introduction of a hard border on the island of Ireland.
So far, the backstop has proved to be a Brexit-negotiated problem.
A no-deal Brexit would mean that Britain leaves the EU and immediately breaks off relations without an agreement.
The United Kingdom would follow the rules of the World Trade Organization if it wants to trade with the EU and others trying to negotiate free trade agreements.
With the UK outside the EU, however, there could be physical checkpoints overseeing people and goods entering or leaving the UK. This is excluded by the Good Friday Agreement, which brought peace in Northern Ireland.
Mr. Gove is one of several new ministers to advance preparations for Brexit since joining Mr. Johnson's Cabinet earlier this week.
In a letter to the Sunday Telegraph, Javid said that 500 new border guards could be "significantly funded" and "possibly" improved infrastructure in British ports.
Javid is expected to pledge more money for the next week's projects.
Boris Johnson's Government
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Meanwhile, there have been reports of more dissatisfaction within the Conservative party as MPs opposed to Brexit agree to continue to think about ways to avoid this
The Observer claims that former Chancellor Philip Hammond has private talks led with Labor Brexit spokesman Sir Keir Starmer before Mr. Johnson became prime minister.
The two met shortly after Hammond's resignation from the government.
Starmer told the paper that work on a "strong bipartisan alliance" to prevent Brexit from escalating without an agreement would "intensify the summer".
But although several Tory MPs expressed their opposition to Mr. Johnson in his first week in Downing Street, an opinion poll suggested a recent increase in support for the party.
Since Mr. Johnson took office on Wednesday Conservatives have jumped 10 points to 30%, according to a Sunday poll.