Also on the agenda are the conflict in Ukraine and Russian sanctions, and preparations for Germany's hosting of a G7 summit in Bavaria in June.
But most attention will focus on what – if any – agreement the pair can come to on leeway for Cameron's desire to achieve better British terms of membership of the European Union, as he faces anti-Brussels sentiment on his right-wing from Ukip – the insurgent party campaigning to leave the EU.
The meeting is expected in Downing Street late afternoon, followed by a joint press conference at around 5.45pm British time. It will be one of the final times the pair meet face-to-face before May's general election in the UK.
Cameron has already seen two of his own MPs defect to Ukip, and promised a full referendum by 2017 on Britain's continued membership if he wins power again in May, in an attempt to stop Conservative voters flocking to the anti-EU, anti-immigration party.
London and Berlin have recently been at odds over plans by Cameron's government to limit immigration from within the European Union.
Merkel reportedly told Cameron in October that he was approaching a "point of no return" with the EU over a proposal to limit the migrant intake from other member states.
Cameron promised tough curbs on welfare for EU migrants in a speech in late November but stopped short of calling for a cap on new arrivals.
Merkel has her own domestic problems in Germany with immigration, as some 18,000 people take to the streets each week in Dresden, and smaller numbers in other cities, to protest against the supposed "Islamization" of Germany.
While in London, Merkel also plans to visit the exhibition "Germany: memories of a nation" at the British Museum which traces 600 years of German history until the 1989 fall of the Berlin Wall.
And on a lighter note, the topic of the Conservative's latest election poster – boasting of the British route to economic recovery, but actually featuring a picture of a German road – may prove an ice-breaker.
A spokesman for the British Embassy in Berlin told The Local: "This is a visit that comes as Germany takes over the G7 presidency, and will focus on British and German priorities for the G7 – including the global economy, the Transatlantic Trade and Investment Partnership, which is important to both countries, and Russia."
However, it was expected that immigration and EU reform will also play a large part in the talks. One source said: "They are two politicians – and they will talk politics."