Among its preliminary conclusions is that the new American leader is a risk-taker who can be naive, according to a senior Kremlin adviser, NBC News reports.
Trump "doesn't understand fully who is Mr. Putin — he is a tough guy," former Deputy Foreign Minister Andrei Fedorov told NBC News.
The file is being compiled by retired diplomats and some of Putin's staff, he added.
The attempt to get inside the U.S. president's mind is aimed at helping Putin plan for his first meeting with America's new leader, the date for which is yet to be decided.
"Very serious preparatory work is going on in the Kremlin, including a paper — seven pages — describing a psychological portrait of Trump, especially based on this last two to three months, and the last weeks," added Fedorov, who said he has known Trump since 2000.
Putin's government is growing increasingly concerned about Trump's battles in Washington, according to Fedorov and former lawmaker Sergei Markov, who remains well-connected at the Kremlin.
Read alsoTrump's team in disarray, U.S. Senator McCain tells Europe – ReutersIt is worried the president will not have the political power to improve relations with Russia, as he has indicated he might try to do, and even, perhaps, lift some U.S. sanctions.
Fedorov said that Trump's "constant battle with the mass media" was "worrying us."
The U.S. president "is dancing on thin ice," he said. "It's a risky game."
A former prime minister under Putin said the Kremlin is taking no pleasure at Trump's struggles.
"Absolutely not — not laughing," Mikhail Kasyanov said. "The situation is very serious and the whole of [Putin's] team, they are nervous."
Many in the Kremlin believe hardliners in America — in Congress and the military — want to sabotage the president and his plans for better ties with Russia.
Read alsoBloomberg: Merkel's efforts to get Trump to take a harder line on Russia may be paying offSome even talk of a conspiracy against Trump. Markov, the former lawmaker, told NBC News that he believes America's intelligence services "want to overthrow President Trump in a coup" because of his desire to improve relations with Russia.
Flynn was a victim of U.S. intelligence services, according to Markov.
So while many in Russia celebrated Trump's election, the mood in Moscow was changing from delight at Trump's election to doubt about his ability to deliver on a better relationship with Russia, he added.
"Donald Trump has done nothing good for Russia, nothing," Markov said. "But they already attack him."