Negotiators from both sides failed to bridge the gap in intense weekend talks before a high-stakes EU summit on October 17-18.
"I think everyone in the UK should have confidence that this prime minister, Theresa May, will never sign a deal that is not compatible with the letter and spirit of the referendum result," Hunt told reporters on arriving for EU foreign ministers talks in Luxembourg on October 15.
"But we also firmly believe that we can find a deal on that basis that works for the European Union and our partners and friends in Europe."