Many suspect that will not be enough time, which has led the European Union to demand a "backstop" to ensure there are no customs posts or other controls along the border between the U.K.'s Northern Ireland and European Union member Ireland.
Tajani said May said she would evaluate an idea to extend the post-Brexit transition period by a year from the current cut-off date at the end of 2020 but that the British prime minister did not say whether she would favour that, or not.
BRUSSELS, BELGIUM - Theresa May has told European leaders she is prepared to extend the Brexit transition period by another year, keeping the United Kingdom tied to EU rules and regulations until at least December 2021.
If a withdrawal agreement is reached, a transition period would kick in after next March, which has been planned to end in December 2020.
This new UK-wide customs backstop could be negotiated in the transitional period - "parallel to the talks on the future relationship", said the Irish source.
But even an extension will not get rid of the EU's insistence that such a backstop must be agreed to secure a deal.
May addressed European Union leaders for 15 minutes before they sat down to a dinner which she did not attend, with her spokesperson briefing that the Prime Minister had urged European Union leaders to show "trust and leadership".More news: Student's cookie recipe may have included grandparent's ashes
In the meantime, the chances of an extraordinary summit being held in November to finalise an agreement have all but vanished as sufficient progress in the talks had not been made.
Tajani said May had offered nothing new, though he thought her "body language" was positive. "But we are defending the single market".
Mr Tusk said: "We are in a much better mood than after Salzburg and I feel today we are much closer to final solutions and the deal".
"One that ensures we don't have any kind of a border and one that protects the peace process, however, we have to have that insurance policy, and Theresa May reaffirmed her commitment to it last night".
The DUP has said it will not sign up to any backstop clause which would create new checks between Northern Ireland and the rest of the UK.
Mrs May's future as Prime Minister appears to be staked on the success of her Brexit negotiations - with infighting within her own party threatening her position. "It doesn't resolve any of the underlying issues and keeps us in a painful Brexit holding pattern".
Tusk has made it clear that if May and Barnier do not signal concrete progress towards a draft deal he will not call a November summit to sign it.More news: Google Pixel 3 Teardown Shows an LG-Made OLED Display: iFixit
And the Financial Times says one of the US's top market regulators has threatened to stop European banks from using American futures markets if the EU refuses to water down post-Brexit plans to oversee clearing houses.
On Tuesday, the chairman of the US Federal Reserve Jerome Powell warned that a "disorderly Brexit" would slow the European Union economy as a whole and have a knock-on effect on US banks. "For now, we have a no-deal", the diplomat said, adding leaders were waiting for Britain's budget, due to be presented to parliament in late October, to be passed.
Lithuanian President Dalia Grybauskaite said that 2 ½ years after Britain's Brexit referendum, the country had still not explained clearly how it wants to leave the EU.
Asked about the plan, a British official said there were no plans to propose a change to the transition.
"Today, we do not know what they want", she said.
It will take place at the same time as a similar rally in London to demand a People's Vote on the terms of the Brexit Withdrawal Agreement.
Mr Corbyn said International Development Secretary Penny Mordaunt and Work and Pensions Secretary Esther McVey have refused to say they backed the Chequers plan, joking: "Maybe she could share a pizza with them and sort it out".More news: Russia Climbs in Global Competitiveness Index