But the Washington-Moscow rivalry has a long history and there are there many points of friction that could yet spoil Trump's hoped-for beautiful friendship.
With the foes at loggerheads over Syria, Ukraine, pipeline policy, espionage and election interference, even Trump cautioned: "I'm not going with high expectations." The brash billionaire property magnate has been president for 18 months, while the 65-year-old former KGB officer has run Russia for the past 18 years.
The 72-year-old president nevertheless has a high opinion of his ability to woo tough opponents, such as North Korea's Kim Jong Un, whom he met at a summit last month.
The Kremlin has also played down hopes that the odd couple will emerge from their first formal one-on-one summit having resolved the issues poisoning relations.
Putin, who played host at the World Cup final in Moscow on Sunday and was due to arrive in Finland later Monday, has remained terse in the run up to the summit.
But on Friday his adviser Yuri Ushakov also played down expectations, saying: "The state of bilateral relations is very bad.... We have to start to set them right."
In the run-up to talks, Trump has refused to personally commit to the US refusal to recognise Russia's annexation of Crimea, leaving open the possibility of a climb-down.
If Washington were to de facto accept Russia's 2014 land-grab, this would break with decades of US policy send tremors through NATO's exposed eastern flank.
Trump's critics in Washington will be watching this -- and also how he handles the growing evidence that Russian agents intervened in America's 2016 presidential race.
Last week US special prosecutor Robert Mueller indicted 12 more Russian intelligence officers for allegedly hacking Trump rival Hillary Clinton's computer server.
"Well, I might. I hadn't thought of that. But I certainly.... I'll be asking about it," Trump told CBS.
Senior diplomat and now chairman of the Council on Foreign Relations Richard Haass said that for centuries world order has depended on "non-interference in the internal affairs of others and respect for sovereignty." "Russia has violated this norm by seizing Crimea and by interfering in the 2016 US election. We must deal with Putin's Russia as the rogue state it is," he tweeted.
But of all the topics that may come up in the meetings it is Syria that may prove most important.
Despite the doubts of his top national security advisers, Trump is keen to withdraw US troops from eastern Syria, where they have been battling the Islamic State.
Reports suggest he may seek a deal that Russia work with Israel to contain Iran's influence, in exchange for allowing Putin's ally Bashar al-Assad to stay in power.
This could free up US troops to withdraw, but would also -- as with Crimea -- mark a major victory for Putin and a betrayal of local US allies on the ground.
In a bitter tweet sent as he flew between his golf resort in Scotland to the Finnish capital, he said even if he was handed the keys to Moscow "it would not be good enough." Helsinki may not be impressed either.
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)