"People like me want to avoid a no-deal outcome, a crashing out on March 29".
"I think we should send the Prime Minister back to Brussels with a strong mandate to be able to say if you compromise with us on this one issue, on the backstop, we would be able to a get an agreement - an agreement that is nearly there", he told BBC Radio 4's Today programme.
European Union officials have been adamant for months, however, that there is no room to renegotiate the so-called "backstop" element of the current draft Brexit plan, which is created to keep the Ireland-Northern Ireland border open regardless of whether a final customs deal is reached.
Bercow said he had selected seven amendments, including one put forward by Conservative lawmaker Graham Brady which calls for the so-called Northern Irish backstop to be removed and replaced with "alternative arrangements".
What are more important are a series of amendments tabled to the motion.
The backstop is is the insurance policy in Mrs May's plan to prevent checks on goods and people returning to the Northern Ireland border, which some MPs fear could leave the United Kingdom tied to the EU's rules indefinitely.
In the process she buys another two weeks of false hope that Brexit deal looms but also massively increases risk of no-deal Brexit.
Speaking on BBC's The Andrew Marr Show, Mr Coveney assured that the backstop is not "dead", and said it is part of a "balanced package".
Labour MP Hilary Benn has one amendment explicitly demanding indicative votes on Brexit options, including Norway Plus, a Second referendum, a "managed" no-deal, or a Labour Brexit.
Tánaiste and Minister for Foreign Affairs Simon Coveney has said the European Parliament will not ratify a Brexit deal that does not have a backstop.
If Theresa May backs the Steve Baker/Nicky Morgan Brexit plan C she probably wins the Brady amendment and defeats Cooper/Boles - but doing so would be based on what she believes to be a lie, since she is (probably rightly) convinced there is zero chance of European Union 27 leaders agreeing on the Morgan/Baker Brexit plan. "We need to go back into the text of the treaty and solve the problem".
It even commands the support of several Remain-supporting Cabinet ministers, with Work & Pensions Secretary Amber Rudd calling on the prime minister to have a free vote on Tuesday's amendments.
May's spokesman said she backed a proposed measure that called for the removal of a controversial Irish border "backstop" arrangement written into the divorce deal.
The PM was also willing to give the parliament another opportunity to vote for the Brexit deal as soon as possible. So it is in fact up to the Speaker of the parliament to decide which proposals will be debated.
Opposition to the backstop by pro-Brexit politicians - who fear it will trap Britain in regulatory lockstep with the European Union - helped sink Mrs May's deal on January 15, when Parliament rejected it in a 432 to 202 vote.
Unless lawmakers agree a way forward or the European Union agrees to extend the negotiating period, Britain will leave without any deal, a scenario that businesses fear will bring chaos to the world's fifth biggest economy. "The Cooper Bill could give MPs a temporary window to agree a deal that can bring the country together".
"The fact we are now staring at the Brexit deadline of March 29 once again as a cliff-edge event has disappointed many in the market who were betting on a sterling recovery", said WorldFirst head of FX strategy Jeremy Cook.
A reporter for The Times said officials on "both sides of Brexit talks" had described it as "no plan at all" and "bonkers".