European Union negotiator Michel Barnier suggested the extension as a way of breaking the deadlock on how to keep Britain's border with Ireland open after Brexit, which is holding up the whole divorce agreement.
He repeated his party's criticisms of the EU's Irish border backstop position.
While it could help May sell a deal at home, it won't remove the need to accept the most controversial part of the EU's proposal - that in a last-resort situation, Northern Ireland could be split off from the rest of Britain.
It's reported in the Irish Independent today that the idea of extending the two year Brexit transition by one year is being considered to provide more time to develop a temporary customs arrangement between the European Union and the UK.
"The point is that this is not expected to be used, because we are working to ensure that we have that future relationship in place by the end of December 2020", the prime minister said.
With the impasse likely to continue, diplomats are beginning to expect that a deal might not be complete until December or January, making it very tight to ratify any agreement in domestic parliaments across the European Union, including the House of Commons.
Talks on finalising the UK's withdrawal agreement and a political declaration on future trade relations with the EU have been blocked by failure to agree on a backstop to avoid a hard border between Northern Ireland and the Republic in the event that an agreement on future EU-UK relations can not be struck.
Tenn. child diagnosed with mysterious illness; 22 states affected
AFM is still extremely rare . "We have not been able to find a cause for the majority of these AFM cases", Messonnier admitted. " Many people will get the infection and very few will get the neurologic disease" that leads to paralysis, Messacar says.
Tusk advised May that "creative" thinking from Britain was required to avoid a hard border on the island of Ireland, the issue that has brought divorce negotiations to a standstill.
After one-on-one meetings with Tusk, European Commission chief Jean-Claude Juncker and Irish Prime Minister Leo Varadkar, May will brief her 27 European colleagues before leaving the EU leaders to discuss Brexit over dinner without her.
There was not enough progress, he said, but leaders had called on the Task Force to intensify work in the weeks ahead.
"There is a message of goodwill, readiness to reach an agreement".
Downing Street insiders do not now believe there is much prospect of the EU27 recommending a special November summit to seal a deal.
One EU27 diplomat told Sky News: "The clock is ticking - the ball is in the United Kingdom court".
Water levels plummet on Texas river that washed out bridge
In 24 hours, the river rose to 12 metres, some 10m higher than the day before, and around 5.5 metres above major flood stage. The Llano River's crest of 39.91 feet in Llano was just below the record high of 41.5 feet there in June 1935.
Mrs May initially suggested an "implementation period" of around two years after Brexit, to give the UK's authorities and companies time to prepare for the new arrangements.
So we need time, we need much more time.
Tajani said May told him she would consider it but gave no indication of whether she favoured such an extension.
The European Union's top trade official is playing down the importance of a USA announcement that it will pursue a trade deal with Britain, noting London can not negotiate such pacts until it leaves the bloc. Today we do not know what they want.
Theresa May has insisted a Brexit deal remains "achievable" at the start of a European summit which has been overshadowed by a set back in negotiations.
The EU is willing to insert a text in to the Withdrawal Agreement a text guaranteeing it will create a UK-wide customs backstop plan in the future.
When they asked her about Brexit, she is said to have responded: "Please, it's a wonderful evening".
President Trump says military will close southern border as migrant caravan approaches
Meanwhile, a Honduran caravan of migrants headed for the United States border has grown to 4,000. Trump said in the first of a series of impassioned tweets on the growing crisis.
Mrs O'Neill said: "In order to preserve her toxic alliance with the DUP, she is trampling over the rights of citizens by acquiescing to that party's refusal to share power (at Stormont) on the basis of equality".