Eurosceptics will claim that Mr Cameron has failed in his flagship bid to stop benefits claims by EU migrants for four years
The two EU leaders have suggested the compromise deal in a bid to save Mr Cameron’s flagging renegotiation and ensure Britain does not leave the EU.
Mr Cameron had initially demanded that Britain is able to stop EU migrants claiming in-work benefits for four years.
However, this was overwhelmingly rejected by EU leaders, who said that it threatened the principle of “freedom of movement”.
The news that Mrs Merkel and Mr Hollande have offered the deal will be welcomed by Downing Street and will allow Mr Cameron to claim that his renegotiation has been largely successful.
However, eurosceptics will claim that Mr Cameron has failed in his flagship bid to stop benefits claims by EU migrants for four years, a plan which he made the centrepiece of his renegotiation strategy.
At a European Council meeting last week, Mr Cameron was told that he would not be able to stop migrants claiming in-work benefits for four years.
However, he made clear to European leaders that he was willing to discuss other options.
The depth of opposition to the benefits curbs has shocked Downing Street and a number of Government sources believed that Mr Cameron would have to abandon the plan entirely.
However, according to the Politico website, Mrs Merkel and Mr Hollande are now “co-ordinating” in order to offer Mr Cameron the compromise of three years.
Mr Hollande had been one of the most vociferous critics of Mr Cameron’s plans.
Downing Street believes that it will be able to make the case that three years will reduce net migration to similar levels to four years.
They hope it will allow Mr Cameron to tell voters that his renegotiation was successful and that they should vote for Britain to remain in the EU.
Mr Cameron has indicated that the in-out referendum on Britain’s membership of the EU will be held next year.
One other potential solution being offered by Brussels is to give the UK an “emergency brake”, meaning that the Government could stop paying migrants benefits for a set period of time if it is able to convince Brussels that the number of foreigners coming to the country is harming public services.