The Dutch newspapers Tages-Enseiger and NRC have said the two Russian men were arrested in the Netherlands in early 2018.
The Russians were expelled Monday from the Netherlands shortly after their arrest, which has not been announced so far.
A spokeswoman for the Swiss intelligence agency, told the BBC that the agency was aware of the details of "the issue of Russian spies", without reference to the laboratory Spies near the Swiss capital, Berne.
The Swiss intelligence confirmed the results of its joint investigation with NRC.
The investigation says the Russians possessed equipment that could have been used to penetrate electronic systems and that they were working for Russian intelligence.
Britain said two Russian intelligence agents carried out the poisoning of Sergey Scrippal and his daughter Yulia in Salisbury County in March.
Scrippel and his daughter survived, but a local woman named Down Stirgs died of exposure to the same toxin a few months later.
NRCN said the two suspected spies, targeting the Swiss laboratory, were different from the two people accused of poisoning Scrippal.