"Let's do a deal", she wrote in the Mail on Sunday newspaper.
The prospect of a cross-party compromise has alarmed many Conservatives, and May acknowledged that it was "not what I wanted, either".
The Conservatives are desperate to move forward after losing hundreds of positions in last week's local authority elections.
The UK was supposed to leave the European Union on 29 March - but the deadline was delayed until 31 October, after MPs rejected Theresa May's withdrawal agreement three times.
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Ce qui est certain, c'est que Roberto Firmino ne participera pas à cette rencontre, comme il l'a expliqué devant les journalistes.
Prime Minister Theresa May addresses delegates during the Scottish Conservatives' annual party conference at the Aberdeen Exhibition and Conference Centre, Friday May 3, 2019.
But suggestions that May's government might make a deal that accepts Labour's demand for close economic ties with the European Union have infuriated pro-Brexit Conservatives, who are demanding May's resignation.
"This is a" judgement on leadership", and with sadness Mr Duncan Smith said it makes May's tenure as a caretaker. "The message was loud and clear that, since March 29, people have decided they are absolutely furious with the political class", he told LBC.
Mrs May is now seeking Labour support to get an agreement through Parliament.
Any customs union would likely upset the most pro-Brexit members of the Conservative Party, while the Observer newspaper reported that scores of Labour lawmakers had written to Corbyn to insist on a second Brexit referendum. "I can't think that any other party in the United Kingdom has raised money like that".
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Despite Mrs May's calls for unity with Labour over a Brexit deal, shadow chancellor John McDonnell said he does not trust the Prime Minister and accused her of having "blown the confidentiality" of cross-party talks.
The Sunday Telegraph carries comments from Nigel Farage, who warned the Prime Minister she would be entering a coalition "against the people" if she agrees to a customs deal with Labour.
"The key thing is the Government want to be able to do their own trade deals and my concern is that if we have a trade deal with the United States, for example, that could mean Trump's America and big private healthcare corporations getting their hands on NHS contracts", he told Sky.
Nevertheless, McDonnell said talks would continue this week and if a deal could still be struck, it must be concluded quickly.
Earlier on Saturday, Buzzfeed News reported sources saying that May was optimistic about a deal, and that behind closed doors the government had already compromised on a customs union.
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Prime Minister Dmitry Medvedev has also ordered a special committee to investigate the disaster, Ria Novosti agency reported. Aeroflot Flight SU1492 returned to Moscow's Sheremetyevo Airport, making an emergency landing, news agency Interfax reported.
"I negotiated with the European Union what I believe is a very good deal for the United Kingdom - a deal which allows us to genuinely take back control of our money and our laws".