An EU leaders' summit is due in Brussels on October 17 and if a deal is close a special Brexit meeting could be called in November to sign off on it.
In an outspoken interview at a crunch point in the Brexit negotiations, the European commission president also lamented that the former Prime Minister, David Cameron, had blocked him from campaigning during the 2016 referendum, The Guardian said.
Her comments came amid reports the Government was considering allowing more regulatory differences between Northern Ireland and the rest of the United Kingdom to ensure a free-flowing Irish border is maintained on the island.
The British Government is expected to table new proposals in a bid to break the Irish border impasse, but a role for the devolved Assembly has been speculated. The EU could not accept a situation, he said, where British companies had access to European markets but were able to outcompete European rivals by lowering labour, product or health and safety standards.
The timing of the document indicates the European Union could end up using it as leverage to force Mrs May to accept a deal on their terms.
However, it's still not clear how this idea would avoid a hard border in Northern Ireland.
Unai Emery steering clear of talk on Aaron Ramsey's future
Asked for his view on the bigger picture of the match , he said: "We are competing very well in these games". Piotr Zielinski has been identified by Unai Emery as a replacement for Aaron Ramsey , reports say.
It comes after Ms Foster emphasised her party's stance on increased regulatory checks down the Irish Sea as a move they will never support, following suggestions of an Irish Sea border as part of a Brexit backstop deal. "The commission, via chief negotiator Michel Barnier, is working day and night, with the Brits and with itself and the member states, to be able to gather enough progress".
The bloc says an emergency fix - or "backstop" - is needed in case these broader trade talks fail or take longer after Britain leaves the European Union next March and the status-quo transition period runs its course at the end of 2020.
Talks are accelerating - and work is expected to continue through the weekend - as both sides are racing to clinch a deal next month.
"To sum it up: Anyone who thought that an end of the Brexit drama is in sight will have to think again", said analyst Thu Lan Nguyen.
Asked if an exit from Brexit was still possible, Mr Juncker said: "That is in the discretion of the British Parliament and the Government".
Britain could not only have a free trade accord like that with Canada but also extremely close relations in security, foreign policy and other areas, Tusk said after meeting Irish Prime Minister Leo Varadkar.