When asked if the government would drop its opposition to the customs union, which Labour supports, Lidington said he thought it was possible to find a "mechanism" where Britain could keep the benefits of the customs union while having the ability to pursue an independent trade policy.
Central among the issues for the talks is whether the government is prepared to give ground to Labour on a future customs union with the European Union - something ministers oppose, but which is a key plank of Labour's Brexit proposal.
He said it is possible to get the benefits of the customs but still have the flexibility for the United Kingdom to pursue an independent trade policy with other countries. "Labour has a different approach", he told the BBC's Andrew Marr Show.
The minister for the cabinet office explained that while the two parties have common goals there needed to be movement from both sides.
However, the European Union has insisted the terms of the UK's withdrawal, rejected three times by MPs, can not be renegotiated - but there is scope to strengthen the political declaration, a document setting out the parameters of the UK's future relations with the European Union, ahead of the new Brexit deadline of 31 October.
Sources suggested a the chancellor, Philip Hammond, could meet the shadow chancellor, John McDonnell.
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"We would hope to take stock of where we are as soon as Parliament gets back after the Easter recess", he said.
"What we will want to move towards is to put before Parliament a set of options - with a system for making a choice and Parliament actually having to come to a preferred option rather than voting against everything", he said.
However, appearing on Sky News' Sophy Ridge On Sunday, former Tory party leader Iain Duncan Smith called the cross-party talks a "recipe for disaster" for his party.
She also insisted if Mr Johnson or Mr Raab are elected as the next Prime Minister, it will confirm the party has moved to the "extremes of the right" of Conservatism. She said she would go as and when the agreement was ratified, which was looking at around about May, June.
"I don't think this question can be allowed to drag out for much longer", he said. "The time to change this is now", he said.
"We've got to deliver the outcome of the referendum. but, the Conservative Party has got to remain a broad church, a national party, and it's got to be talking about things that matter to people in their everyday lives: housing, health service, living standards". "Many of those with their own eye on No 10 aren't a fan of that prospect".