With just six weeks to go before Britain's scheduled departure from the European Union on March 29, Fox dismissed the chances of another popular vote that could overturn Brexit and also dismissed ideas put forward by opposition leader Jeremy Corbyn.
Labour is proposing its own Brexit plan, which would involve the United Kingdom staying in a customs union with the EU, which they say could get the backing of a majority of MPs.
MPs are set to vote again on Britain's Brexit options on February 14.
Should the prime minster fail in her bid to secure concessions from the European Union before her speech, she plans to ask for more time and promise a vote on other Brexit options at the end of February, the Sunday Telegraph and other British media report.
Opponents of the government accuse May of deliberately wasting time so that Parliament will face a last-minute choice between her deal and no deal.
However European Council president Donald Tusk said there was "no breakthrough in sight".
"We can't allow that to happen", Sir Keir said.
On Thursday, Labour will attempt to force the government to hold the final, "meaningful vote" on Mrs May's Brexit deal by 26 February.More news: Cardi B Twerks on a Piano During Electrifying 2019 Grammys Performance
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"No one could responsibly propose this [a no-deal Brexit]".
Representatives from eight finance and insurance trade groups met on Tuesday with the Economic Secretary to the Treasury John Glen, who is working on the government's "global financial partnership" strategy that seeks to boost London's ties with financial trading hubs after Brexit.
MPs voted to replace the controversial backstop with "alternative arrangements" in a vote on amendments to the PM's Brexit deal last month.
But May's office published her reply to Corbyn late on Sunday, showing little appetite for a U-turn which would risk splitting her fractious party by ruling out the scope for Britain to strike its own trade deals around the world.
The Prime Minister received fresh warnings about the impact of Brexit by major business and economic leaders today.
He told the Sophy Ridge on Sunday programme that it would lead to a "very hard border" on the island of Ireland and is contrary to the Good Friday Agreement, the peace deal he helped negotiate which brought an end to The Troubles.
They have also signed a deal to preserve the rights of some 43,000 British nationals living in Switzerland and the 35,000 Swiss residing in Britain after Brexit. The backstop is the main obstacle to securing agreement on the terms of Britain's withdrawal from the EU.