Having spoken by phone on Britain's renegotiation attempts, Number 10 said both leaders recognised the goodwill across Europe for Cameron's demands.
However, they also accepted that both sides needed to work to find solutions.
The phone call came after Cameron held talks with his Irish counterpart Enda Kenny yesterday, in which Kenny said he supported Cameron's treaty change agenda, but could not speak for other countries.
Cameron is currently attempting to woo other European leaders ahead of an EU summit in February, where he hopes to make a deal. If successful, the referendum could be held as early as June.
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However, the Prime Minister has come under pressure from some European leaders who are against the UK restricting in-work and out-of-work benefits to EU migrants, one of Cameron's key demands.
Migration and the need for a strong external European border were also discussed by Merkel and Cameron, as well as the need for cooperation with Turkey.