In the US, Presidential hopeful Donald Trump has repeatedly spoken out against free trade, including the long-established North American Free Trade Agreement which opened up trade with Canada and Mexico in the 1990s.
"With the state we're in, we're not even in a position to take in a city state", said Gabriel, leader of the Social Democrats (SPD) - the junior coalition partner in Chancellor Angela Merkel's government.
The deal known as CETA was formally concluded in 2014 and requires the approval of 28 EU member states and European Parliament.
He said that during the talks neither side had agreed on a single common chapter out of the 27 being deliberated.
Nonetheless, Mr Gabriel is an important voice and his view that TTIP has in effect failed is a sign of just how much political difficulty it faces, our correspondent added.
She suggested she was open to changes in the EU's planned quota system, which aims to transfer of about 160,000 asylum seekers from Greece and Italy to other European Union states, but said it was important to find a solution that shared responsibility. "Roll on US-UK trade talks!"
"Though the Brexit vote was shaped by concerns about the free movement of labour, rather than of goods and services, the appetite for new trade deals was already weak". These comments were interpreted by British pundits as a thinly veiled threat and the idea that Brexit would free the people from the unpopular trade deal became a major rallying cry for the Leave campaign which jumped almost 5 points in polling following the comments.
Washington's attitude appears to have softened after the vote to leave the European Union, with secretary of state John Kerry indicating that preliminary talks on trade could take place although no agreement could be signed until Brexit had actually happened.