"We think that the public came to clear view in 2016 - with all parties and both campaigns having said to them, 'your decision is going to be final'".
Lidington said the government believed it was possible to gain the benefits of a customs union without losing the power to strike independent trade deals.
"What we have found in terms of objectives... there is fair bit that both parties would have in common", he said.
Sources suggested a the chancellor, Philip Hammond, could meet the shadow chancellor, John McDonnell.
"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.
May and Corbyn will continue talks this week after the prime minister secured an extension to the Article 50 deadline on Wednesday.
May has come under fire from MPs including former leader Iain Duncan Smith following her decision to agree an extension that would result in the United Kingdom taking part in European elections next month.
Accepting this would mean the Prime Minister has to tear up a key red line and risk splitting her party. She said she would go as and when the agreement was ratified, which was looking at around about May, June.
"I think the date isn't October".
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"I don't think this question can be allowed to drag out for much longer", he said.
The hardline Brexiteer and former Tory leader added that a grassroots revolution had begun with many MPs unwilling to fight in the European elections.
"It hasn't changed", he said.
However, the former party chairman Sir Patrick McLoughlin warned those agitating for a swift leadership change that installing a hard Brexiter in No 10 would not necessarily solve the party's electoral problems.
Nigel Farage's new Brexit Party is attracting support from disgruntled Conservative voters unhappy at the party's failure to deliver Britain's departure from the European Union, according to new polling.
"But the only way to cure our Brexchosis is to do what we promised the people - to leave the European Union, and do it properly".
He said meetings later this week would be divided into different subjects led by relevant ministers and their Labour opposite numbers.
"It was on the 29th when we didn't leave; that's when this has all gone wrong".