Mr Grieve had originally wanted the amendment to say that the government must seek the approval of Parliament for its course of action - and that ministers must be directed by MPs and peers in the House of Lords.
The Government's current proposal would neuter Parliament if the Government failed to reach a Brexit deal.
Pro-EU Tories have warned they remain ready to rebel if their demands are not satisfied by the compromise amendment while leading Brexiteer Jacob Rees-Mogg claimed their idea made a "no-deal Brexit" more likely.
The motion would be unamendable, meaning that MPs could not insert a requirement for May to go back to the negotiating table or extend the Brexit transition.
Grieve said: "I can't save the government from getting into a situation where parliament might disagree with it". And the next day I stood up in Prime Minister's Questions and said I'd put an amendment down in the House of Lords.
The row is over what role Parliament should have if the Brexit negotiations look like failing.
Negotiations on a compromise, promised last week by May to avert a defeat, fell apart at the last minute on Thursday when rebels said the government had changed the wording of an agreement.
However, the Grieve amendment was not put to a vote on Tuesday, after would-be rebels accepted "personal assurances" from the PM that a compromise would be found.
Brexit supporters on the 1922 Committee - made up of Tory MPs who do not hold Government positions - were swift to react once the implications of these concessions became clear, with one senior Leaver remarking: "If Theresa and [Chief Whip Julian Smith] have sold us out here they are in real trouble".More news: US Open: Should Phil Mickelson have been disqualified for penalty?
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Speaking in parliament on Wednesday, May said the government could never allow the hands of the government to be tied in the negotiations or allow the Brexit decision to be reversed.
May's Conservatives do not have a majority in the unelected House of Lords, and with the opposition Labour Party deciding to back a rival proposal, the government faces defeat when the debate begins on Monday afternoon.
It followed a strained parliamentary session, where the deep nationwide divisions opened up by Britain's vote to leave the European Union in 2016 were on display, with pro-EU lawmakers saying they had received death threats.
Potential rebels in the Conservative party met the Prime Minister last week as she tried to prevent the House of Commons voting through an amendment which would allow a vote on a "no deal" Brexit. "Grateful for the conversations but without consultation what was agreed earlier today has been changed".
"Would be amusing if only it wasn't such a serious issue".
The government's prospects of defeat were increased last week when the junior justice minister Philip Lee resigned his post so he could vote against the minister on a meaningful vote.
Shadow Brexit secretary Sir Keir Starmer said: "The Government's amendment is simply not good enough".
Liberal Democrat Brexit spokesman Tom Brake said: "It appears Theresa May has been caught red-handed making conflicting offers to Tory rebels and hard-right Brexiters. And therefore it can not be accepted". It was clear she couldn't keep both promises - we are now finding out which lie she was telling.