As reported by Censor.NET, this was announced by The Financial Times.
According to the newspaper, several people who used to work with Kilimnik say it was an open secret among the Manafort team and at a previous employer that Kilimnik, an army-trained linguist, had a background in Russian military intelligence.
At the time, the connection was deemed unimportant - Mr Kilimnik was valued for his "excellent English", these people say.
Today, with Mr Kilimnik still close to Mr Manafort, according to people who know both men, the links have taken on new significance. As Russian president Vladimir Putin likes to joke, there is no such thing as a former intelligence officer.
Revelations about Mr Kilimnik threaten to deepen the controversy over Mr Trump's sympathetic comments towards Moscow and Mr Putin on the campaign trail - giving him a reputation as the US's first pro-Russian ticket - and over Mr Manafort's work for Mr Yanukovich, who was toppled by Ukraine's 2014 Maidan revolution.
People close to Mr Manafort insisted that his resignation from Mr Trump's campaign had nothing to do with adverse publicity over his Ukrainian activities. Mr Trump's campaign directed all questions about Mr Manafort's relationship with Mr Kilimnik to Mr Manafort.
But one person with intimate knowledge of Mr Manafort's operations said that the relationship was grounds for concern.
"It's a very real issue if you have a known Russian intelligence officer one degree of separation from Donald Trump, presidential candidate," he said. "Konstantin Kilimnik knows Paul very well, and Paul is at Trump's right hand."
Born in Ukraine in 1970, Mr Kilimnik served in the Russian army. His first long-term job after leaving the military was as a translator in Moscow with the International Republican Institute, the US non-governmental organisation that promotes democracy, in the early 1990s. One former IRI employee said he was hired along with another military-trained linguist because of their proficiency in English.
"We knew that they were Russian military intelligence because that's where they learned their English. It wasn't a big deal," this person said.
But another former IRI staffer said that Mr Kilimnik's background was a cause of concern for some staff, and it was assumed that he continued to inform Russian intelligence.
Yet another said that there were suspicions that he had connections to Russian intelligence, and that sometimes he appeared to engage in activities that were unrelated to his job.
This person said the institute did not act on the suspicions because there was no hard evidence and because there was nothing about Mr Kilimnik's IRI-related work that was secret and would be comprised if disclosed to Russian intelligence.
A decade later, Mr Kilimnik's language skills led to his recruitment as an interpreter for the Manafort team advising Rinat Akhmetov, Ukraine's richest man, on an image makeover. He remained with the team when it switched to advising Mr Yanukovich's Party of Regions, of which Mr Akhmetov was a backer.
One team member at the time said Mr Kilimnik's intelligence background was known about, as at IRI, and some suspected he was reporting back to Moscow, but this was again considered unimportant.
The interpreter was gradually entrusted with more duties as the team helped Mr Yanukovich recover from his disgrace after Ukraine's 2004 Orange revolution to win the presidential election in 2010.
"It was well-known, I think, that he had some sort of intelligence background but that was never an issue for us because the embassy did not have much contact with Manafort's operation," a US official with experience in Ukraine recalled.
Mr Kilimnik also played a role in business dealings that Mr Manafort's team pursued with two of the region's richest oligarchs, Russia's Oleg Deripaska and Ukraine's Dmytro Firtash, former associates said. When Phil Griffin, who had run Mr Manafort's Kyiv office, left the team in 2011, Mr Kilimnik took over his position.
The Russian kept such a low profile that there are no known photographs of him on the internet. Acquaintances describe him as a highly intelligent, suave and polyglot communicator, and skilled political analyst.
Ukrainian politicians are now raising concerns about Mr Kilimnik's proximity to Mr Manafort and through him, a potential next US president, when east-west tensions are again rising.
Volodymyr Ariev, a pro-presidential MP, on Friday submitted a formal request for an investigation into Mr Kilimnik's past. "Given his biography, this individual could be linked to Russian intelligence services," he wrote in a letter to Ukraine's general prosecutor Yury Lutsenko.
His letter came hours after Ukraine's anti-corruption bureau published copies of entries totalling $12.7m to Mr Manafort in an alleged ledger of off-the-books payments from Mr Yanukovich's Party of Regions to political advisers, pundits and campaigners.
The bureau stressed, however, that it had not established if Mr Manafort actually received the payments. Mr Manafort this week denied ever receiving cash payments from the party.