"In view of the United States' state of mind today, that seems to be the most likely option," minister of state for trade Matthias Fekl told French radio when asked if the talks on a Transatlantic Trade and Investment Partnership, which began in 2013, could stop.
Fekl's comments reflect deep suspicion in Europe that the deal will erode ecological and health regulations to the advantage of big business.
Washington and Brussels want the mega-deal completed this year before US President Barack Obama leaves office, but it has faced mounting opposition on both sides of the Atlantic.
On Monday, environmental pressure group Greenpeace released a trove of leaked documents about the closed-door negotiations, charging that a deal would inflict a dangerous lack of standards on US and European consumers.
However, the European Commission, which negotiates trade deals on behalf of the 28 EU member states, said Greenpeace was "flatly wrong" in its interpretation of the documents.
The Greenpeace leak was a "storm in a teacup," Brussels said.
US officials also hit back at Greenpeace with the US Trade Representative saying:
"The interpretations being given to these texts appear to be misleading at best and flat out wrong at worst."
Fekl said that Europe was pushing for "reciprocity."
"Europe is offering a lot and we are getting very little in return. This is unacceptable," said Fekl, who negotiates trade deals on behalf of France.
"It is a deal that -- in the state it is in today -- would be a bad deal," he said.