The TASS news agency reported that Bolton had discussed potential cooperation between the two countries' security councils with Yuri Averyanov, the first deputy secretary of Russia's Security Council.
Bolton, who last year accused Putin in Britain's Daily Telegraph newspaper of "lying with the benefit of the best KGB training," then began talks with Russian Foreign Minister Sergei Lavrov ahead of his planned sit-down with Putin.
Trump congratulated Putin by phone in March after the Russian leader's landslide re-election victory and said the two would meet soon. However, the Russians have since complained about the difficulty of setting up a meeting.
Relations between Washington and Moscow are languishing at a post-Cold War low. They are at odds over Syria, Ukraine, allegations of Russian interference in the 2016 US presidential election and accusations Moscow was behind the poisoning of a former Russian spy in Britain in March.
Expectations for the outcome of any Putin-Trump summit are therefore low, even though Trump said before he was elected that he wanted to improve battered US-Russia ties.
A special prosecutor in the US has indicted Russian firms and individuals for meddling in the presidential election to benefit Trump, and is investigating whether anyone in Trump's campaign helped the Russian effort. Trump denies wrongdoing and calls the investigation a "witch hunt."
The Kremlin said on Wednesday that Putin and Bolton would discuss what it described as "the sad state" of the US-Russia relations.