Barley, a German-British MEP, admitted to German public broadcaster NDR that talks had become "increasingly hard".
Failure to strike a deal would see Britain and Europe revert to World Trade Organization terms.
The UK had imposed a deadline of last week's European Union summit for a deal and Prime Minister Boris Johnson said he was now ready to walk away and prepare for a no-deal exit, after five decades of European Union membership.
"The trade talks are over".
Barley, who sat in the Bundestag from 2013 to 2019, does not believe the trade talks will be extended past the EU's mid-November deadline.
Gove has previously said that while the British government wanted an agreement with Brussels, it was not going be "held hostage".
The EU's chief negotiator, Michel Barnier, was due in London for talks on Monday with the UK's chief Brexit negotiator David Frost, but the United Kingdom said this would be pointless without a significant change in direction from Brussels.
But Mr Barnier's trip to the British capital was confirmed by European Commission president Ursula von der Leyen, who said: "As planned, our negotiation team will go to London next week to intensify these negotiations".
Britain wants to reassert sovereignty over its waters and have no European Union legal oversight over the deal - insisting it wants a simple trade deal of the kind the European Union signed with Canada.
It comes as business said a deal was vital to help the post-Covid recovery.
European Council President Charles Michel is seen at a special EU Council summit in Brussels.
Mr Johnson said Britain could embrace the prospect of trading on WTO terms - with tariffs on many goods and some quota restrictions - with "high hearts and complete confidence".
However, industry reacted with alarm, warning of the damage to an economy already stricken by coronavirus if there was no deal by the end of the year.
"What we have seen and what our negotiators have found is that the European Union side have not been willing to produce the detailed legal text, they have not been willing to intensify the talks in a way that would indicate that they were acting seriously about reaching an agreement".
"Neither side can afford to fall at the final fence".
Business leaders are already anxious about the prospect of a no deal, warning it would have a "devastating impact" on jobs across the board.
Asked if he was walking away from talks, Johnson said: "If there's a fundamental change of approach, of course we are always willing to listen, but it didn't seem particularly encouraging from the summit in Brussels".
"We are determined to reach a deal but not at any cost".
"The state of our talks is not that we are stumbling over the issue of fishing, which is the British's tactical argument, but we're stumbling over everything".