Police apprehended two suspected Russian intelligence agents in Davos last August, a Swiss newspaper reports.
Tages-Anzeiger says the men, who had diplomatic passports, may have been preparing a spying operation targeting the World Economic Forum (WEF).
It adds that the pair, one of whom was posing as a plumber, were subsequently released.
Swiss police confirmed to the BBC that two Russians were "checked" in August 2019.
The Russian embassy in Bern told the BBC that the newspaper was just trying to "whip out a scandal out of nothing".
The annual WEF gathering in Davos, which brings together leading politicians and business leaders from around the world, opened in the Swiss town earlier on Tuesday.
In a separate development, US-born financier Bill Browder, who is in Davos, told Reuters the Swiss security service had foiled a Russian operation that targeted him last year.
Mr Browder, a high-profile critic of Russian President Vladimir Putin, said he had been told about this by the security service.
On #DavosToday, @BillBrowder told @AxelThrelfall that the Swiss security service foiled a Russian operation that targeted him. 'They were posing as plumbers - when they were arrested, they presented their diplomatic passports and left the country' #wef20 #reutersdavos pic.twitter.com/JjH8IIkDPi— Reuters (@Reuters) January 21, 2020
Mr Browder is widely credited with the creation of the Magnitsky Act - a 2012 range of sanctions from the United States on top Russian officials accused of corruption.
The act was named after his former lawyer, Sergei Magnitsky, who uncovered an alleged tax fraud in Moscow - and died in a Russian prison in 2009.
What did the Tages-Anzeiger say?
In its report, the German-language newspaper said the two Russians were stopped and checked by police in August.
It said they were suspected of having "carried out preparatory work" for spying on the WEF.
The police in the Graubünden canton became suspicious when they learned that the two Russians had planned to stay for three weeks in the expensive Alpine resort.
Tages-Anzeiger did not name the two suspected agents, or specify what kind of spying operation they had reportedly been preparing.
What did the Graubünden police say?
Graubünden police spokeswoman Anita Senti confirmed to the BBC that two Russian nationals were "checked" by police in August.
Ms Senti said they both had diplomatic passports.
She added that a number of people were being regularly checked for documents in the area, without providing any further details.
And what about the Russian embassy?
Stanislav Smirnov, the press attaché of the Russian embassy in Bern, told the BBC that the diplomatic mission in the Swiss capital had only learned on Monday from the local media about the August incident.
Mr Smirnov said Tages-Anzeiger was trying "to whip out a scandal out of nothing" and wanted to catch "a popularity wave".
The diplomat added that he had no information about the two Russian nationals questioned in August.
In 2018, two Russian men were arrested on suspicion of spying on a Swiss laboratory investigating the poisoning in March earlier that year of Sergei Skripal, a newspaper investigation claimed.
The Swiss lab in Spiez, near Bern, analysed samples from the poisoning of the former Russian double agent and his daughter in the UK.
It has also dealt with evidence of suspected chemical weapons use from the war in Syria.
Russia made no comments on the issue at the time.