"I will not let that happen".
The suggestion, made "personally" and not on behalf of the committee, was received "courteously", he said, but Brussels is waiting for May to say what she wants.
Jacob Rees-Mogg, who leads the anti-EU European Reform Group of Conservative MPs, said that they would not back May's deal, even if she secured a unilateral exit clause, or a time-limit, to the controversial Brexit backstop.
Theresa May is due to meet European Commission president Jean-Claude Juncker in Brussels on Thursday.
On Wednesday Mrs May will hold talks with Northern Ireland's political leaders including the DUP's Arlene Foster, who has promised to tell the Prime Minister the proposed border backstop "drives a coach and horses through the Belfast Agreement's principle of consent" and would effectively create a new border between Northern Ireland and the rest of the UK.
There was immediate concern from Conservative Brexiteers over Mrs May's apparent indication that she was instead seeking "changes" to the backstop arrangement, meant to keep the border open if no broader trade deal is reached after Brexit.
"All of those are being taken forward urgently".
In Belfast today Mrs May also said recent joint United Kingdom and Irish commemorations to mark the sacrifices of the First World War demonstrated the strength of the bilateral links. "I think to extend simply because we hadn't reached an agreement would not provide any impetus for that agreement to be reached".
"We have been very clear there will be an insurance policy". Mrs May said pledges made in the joint report in December 2017 were made in "good faith" and said the British government will honour the principles of the Good Friday Agreement.
May, on a visit to Belfast on Tuesday, tried to reassure Northern Ireland that she can deliver an orderly Brexit that will ensure peace in a province riven by three decades of sectarian conflict until a 1998 accord.
Meanwhile, former Northern Ireland first minister Lord Trimble is threatening legal action over the Irish backstop, which will prevent the return of a hard border.
A government source said the evacuation plans were part of "sensible planning" for Brexit.
It sparked a snap election, but since then, various talks processes have collapsed and the Northern Ireland Secretary Karen Bradley had to take control of financial matters and pass its budget bills through Westminster.
She noted how the Irish government had suggested the creation of annual meetings, where bilateral discussions ministers, the Taoiseach and the Prime Minister, to improve and develop Irish-UK relations.
Barnier has already said the backstop and the Brexit deal negotiations will not be re-opened.
British Prime Minister Theresa May said today that she has directed the Home Office to "urgently" look into how Brexit is affecting citizens rights in Northern Ireland.
Asked by Business Insider last week whether the government was aware of any technology that could avoid the backstop, the prime minister's spokesman said that "we want to begin exploring exploring these options as soon as possible".