The British minister predicted that negotiations with other European leaders to secure a reform deal for the bloc "would go to the wire" at a European Council summit on Thursday and Friday.
British Prime Minister David Cameron is trying to force changes in four main areas, the most contentious being limiting access to welfare benefits for EU migrants for their first four years in the country.
"There isn't a deal yet," Hammond told BBC's Andrew Marr Show. "We have to make progress, there are blanks in the text.
"I don't think that's going to get resolved before Thursday," he added. "We've got a negotiation that will run through this week and I have no doubt that will go right to the wire."
Hammond accepted that Britain might get "slightly less than we expect" in some areas, but stressed that European leaders "understand we have to have a robust deal if the British people are to vote to remain within the European Union."
Hammond said that Britain would not necessarily push for a treaty change to lock in the reforms, saying it wasn't essential to give them binding force, and that it would push back the proposed referendum date if it wasn't happy with this week's proposals.
But if Britain did eventually vote to leave, it could spell crisis for remaining members of the EU, and lead to bitter break-up negotiations, he said.
"Britain has been an enormously important influence in Europe, for open markets, free trade and a less dirigiste approach to running the economy.
"There's a real fear in Europe that if Britain leaves, the contagion would spread," he added.
"Countries remaining in the EU will be looking over their shoulder at the people in their own country going 'if the Brits can do it why can't we?' and they will not have an interest in demonstrating that we can succeed outside the EU.
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