He said: "Four decisions need to be made: MPs should vote against no deal; they should vote against the Prime Minister's deal; the European Union should be asked to extend Article 50 deadline to stop the United Kingdom crashing out in March; and MPs should come together to support a new referendum on European Union membership".
The prime minister has already postponed a House of Commons vote on her plan once - in December - to avoid defeat, and looks certain to see it rejected by MPs on Tuesday amid fierce opposition.
The PM has said failing to deliver on the result of the 2016 referendum would be "unforgivable" and a "catastrophe" for democracy.
But he told Marr: "My own view is that I would rather get a negotiated deal now, if we can, to stop the danger of a no deal exit from the European Union on the 29th March, which would be catastrophic".
"Some of you put your trust in the political process for the first time in decades".
Writing in the Sunday Express, Mrs May said the Commons vote on her Brexit withdrawal deal would be the "biggest and most important decision that any MP of our generation will be asked to make".
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"So my message to Parliament this weekend is simple: It is time to forget the games and do what is right for our country".
"What Article 50 says is: "The EU Treaties shall cease to apply to the State in question from the date of entry into force of the withdrawal agreement or" - and here's the key - "failing that, two years after the notification" so the notification was the letter that was delivered that Theresa May spoke about".
"I'm not saying for one minute that the whole economy will grind to a halt, but there are very specific industries in this country for which a no deal Brexit will have an immediate negative impact".
Mr Grayling also said: "I have not asked for military support for the operations in Kent - that will be handled by Highways England and Kent Police".
The vote had been scheduled to take place in December but was called off at the last minute by the prime minister, who was facing nearly certain defeat.
"As politicians, we've got a responsibility to have a conversation with everybody that we now know that Brexit is going to be painful".
Following a vote in the Commons last week, MPs will also have the right to amend any second proposal brought forward by the British leader. However, with more than 100 Tory MPs opposing the deal, it is expected to be rejected.
Meanwhile, London mayor Sadiq Khan has written in the Observer suggesting that Mrs May should step down and call a general election if she loses next week's vote.