Brussels is understood to have offered Mr Cameron a watered down “emergency brake” Brussels allowing him to stop migrants claiming benefits in the UK for four years – but only if European leaders give him permission.
It is believed that the EU is now proposing that Britain will be allowed to deny benefits to EU migrants coming to the UK for up to four years if he is able to convince Brussels that UK public services are being put under strain because of foreigners.
Mr Cameron had pledged that as part of his renegotiation with Brussels he would stop all EU migrants coming to the UK from claiming in-work benefits until they have lived in the UK for four years.
Tory eurosceptics have said that deal is a “bad joke” and an “insult to Britain”.
Speaking at an event this week organised by Prospect, Mr Hammond said: “First of all as a politician, I do not want to support a proposition that is then going to fail when it’s put to the British people.
"And my judgement is that unless there is, within this package, measures that will have this effect of reducing net migration into the UK from the EU... we have no chance of persuading the British people to support the package in the referendum."
He added: "Therefore it’s a requirement. It’s a necessary condition for a package to be recommendable."
Net migration - the difference between the number of foreigners coming to the UK and those leaving - has soared to around 180,000 last year.
The Government had pledged to reduce it to "the tens of thousands". Eurosceptics have warned that even restricting migrants' access to in-work benefits will do very little to reduce net migration.
Ahead of his visit to Brussels, the Prime Minister warned that the deal currently on the table is not good enough.
He said: “I’m encouraged that ideas are coming forward that have some force, but we’re not there yet. They’re not yet strong enough.”
Mr Cameron added: “There’s going to be a lot of hard negotiation, a lot of hard talking, but it’s encouraging that what I was previously told was impossible is now looking like it’s possible.
“But I wouldn’t agree to something unless it has the force and the weight that we need to solve the problems that we have. I’m prepared to be patient. We don’t need to have our referendum until the end of 2017 but we’re actually seeing the European Union responding to the issues put on the table by Britain, and that’s encouraging.”
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