Stefan Meister, a Russia expert at the German Council on Foreign Relations, said that there is "an increased interest on both sides to talk about topics of common interest" and that, in part because of Trump, the two sides have shifted focus from earlier meetings that focused on Russia's conflict with Ukraine.
Merkel was a leading supporter of sanctions against Russia over its annexation of Ukraine's Crimea region.
The two leaders are far from being allies, however. Meister wrote in an analysis for the council that the talks will still involve "hard bargaining" from Putin's end and neither side is likely to make significant compromises — but both could send a signal that they will "not let themselves be pressured by Trump."
The background to this meeting includes Trump's announcement that he plans to impose sanctions on Russia in response to the poisoning of former Russian agent Sergei Skripal and his daughter Yulia in Britain.
A first set of sanctions would target US exports of goods with potential military use starting August 22, while a second set of broader sanctions could take effect 90 days later if Russia does not confirm it is no longer using chemical weapons and allow on-site inspections. Russia has denied involvement in the poisoning.
Meister said that Putin can use the meeting to "send a signal to Washington that there are allies of the US that still do business with Russia." Beyond that, he can push for Germany and the European Union not to support further sanctions, particularly a second round that might hit businesses working with the Nord Stream 2 project.
The project would add another natural gas pipeline under the Baltic Sea, allowing more Russian gas to bypass Ukraine and Poland.
Trump has criticised Nord Stream 2 and the gas supplies, saying German is "totally controlled" by Russia by being dependent on the energy.
Trump's criticism was linked to his push for other NATO member countries, particularly Germany, to pay a bigger share of the cost of NATO's common defense.
From her end, Merkel will push for a Russian commitment to keep at least some gas transiting Ukraine, which earns transit fees from it. Putin has said he's open for shipments to continue if Ukraine settles a gas dispute with Russia.
Germany also has a strong interest in seeing some of the Syrian refugees in Germany return home in any settlement of the civil war in their home country, and could seek Russia's support for that with President Bashar Assad.
Russia has backed Assad with military force. Putin has pushed Germany and other Western nations to help rebuild Syria's economy ravaged by more than seven years of civil war, arguing that it would help encourage refugees from Syria to return home, easing the pressure on Europe.
Merkel's decision to allow in a flood of refugees in 2015 led to a backlash against her immigration policy and boosted the anti-immigration Alternative for Germany party.
Both Germany and Russia have expressed a desire to maintain the agreement with Iran to limit its nuclear program in return for easing some economic sanctions.
Trump has pulled the US out of the program and imposed new sanctions, saying that they will also hit foreign countries that keep doing business with Iran.
Merkel and Putin have met and spoken by phone numerous times since she became chancellor in 2005. They share some common background.
Merkel grew up under communism in East Germany, as Putin did in the Soviet Union; she speaks Russian and he speaks German after living in East Germany as a KGB agent during the Soviet era.
That said, the relationship is characterised by hard bargaining over each side's national interest.
- AP