Some of the ministers have agreed that they will step down if May backs the idea of remaining in the EU Customs Union or convinces Conservative lawmakers to support the holding of elections to the European Parliament in the country in May, the news outlet reported on Sunday.
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At the same time, at least six anti-Brexit ministers have decided to resign in case May endorses the idea of a disorderly no-deal Brexit, the outlet added.
UK citizens voted to leave the European Union almost three years ago, however, London missed the withdrawal deadline on Friday as May has failed to secure support for her Brexit deal in parliament.
UK lawmakers have already rejected the idea of leaving without a deal, but they cannot agree on the adoption of the prime minister's divorce deal either, as it was rejected on Friday for a third time over the past three months.
The European Union has given the United Kingdom until April 12 to figure out alternative withdrawal arrangements, or leave without an accord on this very day.