Theresa May is considering a plan to delay Brexit and stop the U.K. leaving the European Union with no deal next month, according to people familiar with the situation.

The prime minister is expected to allow her Cabinet to discuss extending the deadline beyond March 29 at a crunch meeting on Tuesday, one of the people said. May would then reveal the Cabinet's conclusions in an announcement to Parliament later in the day.

While no final decision has been taken, putting off the U.K.'s scheduled withdrawal from the EU would be a huge political gamble. On one hand, it would avert mass resignations from pro-EU ministers in May's team. But it would also risk a destabilizing backlash from euroskeptic Conservatives.