Carwyn Jones said an agreement could be reached by "stepping over" red lines.
Negotiations in the meantime are ongoing in Brussels this week.
While Mrs May faces a session in front of the Liaison Committee, made up of senior MPs who chair Commons select committees, a debate will take place in the main chamber on the future relationship between the United Kingdom and EU.
EU affairs ministers will soon have their first chance to discuss the UK's white paper, the UK's policy on its relationship with the EU after Brexit, and how they would tackle key issues, such as trade between the EU and UK.
This time, it was pro-EU legislators from both May's Conservative Party and the opposition Labour Party who tried to derail the prime minister's plans for post-Brexit trade relations with the EU.
The paper also proposes a new customs arrangement with Brussels, whereby the United Kingdom would collect tariffs on behalf of the European Union for goods ultimately going there.
We talk to David Davis, who resigned from the cabinet over the Prime Minister's Chequers blueprint, Tory Remainer Antoinette Sandbach, and Tory Brexiteer Desmond Swayne.
A defeat on the trade bill, central to May's Brexit strategy, had the power to set in motion events which may have toppled the Government.
"There are many flaws in the proposals and far too many questions remain unanswered".
"Facing more committed and hardline opponents - and more of them - than I had".
The move has led to accusations that Prime Minister Theresa May is hoping to abate Tory infighting over Brexit by sending everyone home early.
Today, he's still warning about the possibility of the United Kingdom and the European Union failing to reach a deal, but now he's calling on officials in Brussels to blur their negotiating "red lines".
MPs backed an amendment proposed by Tory ex-minister Phillip Lee, and supported by a cross-party group of MPs who are also doctors, by 305 votes to 301.
"Vauxhall is an inner city constituency whose diverse, multi-cultural and multi-racial community have suffered eight years of Tory cuts and austerity, yet our MP is voting to prop up that Tory government and for a Tory Brexit which threatens job, peace in Northern Ireland and the future of the NHS".
The vote also demonstrated the vital importance of the four or five Labour Brexiteers who have repeatedly defied their own party whip and voted with the government.
A spokesman said: "As set out in the White Paper, the United Kingdom is seeking participation in the European Medicines Agency".
However Brussels has repeatedly said the United Kingdom can not "cherry-pick" its way out of the EU.
European Union leaders urged preparedness for a possible no deal when they agreed at their summit last month to "step up their work on preparedness at all levels and for all outcomes".
"I have had the same views on the European Union since being elected and they knew these views as they were always in my election addresses".
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