Gauke said the prime minister was "reflecting" on the possibility of bringing it back to Parliament for a fourth vote.
The eight options include a no-deal exit, preventing a no-deal exit, a customs union, or a second referendum.
The Conservative Party's chairman Brandon Lewis said he was aware of it but had not seen it.
But her spokesman said she did not believe this would be "in the interests of the country".
Data from the last three votes may shed some light.
The government lost by 344 votes to 286.
Downing Street sources have suggested the prime minister has not given up hope of getting it through the Commons, pointing out that the scale of the defeat was significantly smaller than in the previous two votes. The country's ruling Conservative Party is fractured by an undeclared leadership contest.
The House of Commons is scheduled to vote Monday on a variety of Brexit options, with two ideas - staying in the EU customs union and holding a second referendum on Brexit - emerging as the most likely alternatives.
A version of this proposal received the most support in the first round, falling just six votes short of a majority.
The customs union allows businesses to move goods around the EU without checks or charges.
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Democrats have been demanding the release of the special counsel's full report, as well as the evidence behind it. Once the full report is released, Napolitano said , Trump's opponents will have a "field day".
The motion proposes United Kingdom membership of the European Free Trade Association and European Economic Area.
"There's lots of jockeying for position going forward once the deal has been done and once we have left, but nobody wants to carry the can at the moment".
He said: 'I would rather leave the customs union but we also have to recognise that my party does not have the votes to get the manifesto commitment through the Commons.
British Labour leader Jeremy Corbyn on 30 March.
"I think it's very telling that the Article 50 withdrawal agreement is increasingly called Theresa May's deal so it makes it clear exactly where the blame lies when things go wrong".
Nicky Morgan, a former cabinet minister and Tory MP, said one way to end the Brexit deadlock could be a government of national unity - which is a cabinet made up of different parties.
Mr Lewis told Radio 4's Today programme: "The government's position is very clear - we do not support these options".
Britain has until April 12 to tell the European Union whether it will extend the delay, cancel Brexit or go through without a deal.
If the deal had passed, a Brexit on the terms it laid out should have taken place on May 22nd - but it was defeated yet again, by 58 votes. But the deputy leader of the opposition Labour Party, Tom Watson, said his party was on election footing.
May has blamed MPs, but they say it is her refusal to change course that is blocking any solution.
Potentially another round of "indicative votes" will be held on Wednesday.
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