The BBC and other outlets named the victim as 66-year-old Sergei Skripal, who was hospitalised in intensive care Sunday along with an unidentified woman, in the English city of Salisbury.
Some news reports claimed the pair had been exposed to a deadly opioid in the incident.
A former colonel with Russian military intelligence, Skripal was sentenced to 13 years in jail in Russia in 2006 on charges of spying for Britain, but was granted refuge in the UK following a spy swap between the United States and Russia in 2010.
They remain in intensive care while a "multi-agency response" has been coordinated, Craig Holden, Temporary Assistant Chief Constable of Wiltshire police, said in a statement.
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"Alongside our partner agencies, we are conducting some extensive enquiries to determine exactly what led to these two people falling unconscious and clarify whether or not any criminal activity has happened," he added.
"The pair, who we believe are known to each other, did not have any visible injuries and were taken to Salisbury District Hospital.
"They are currently being treated for suspected exposure to an unknown substance" he said, adding that they were "in a critical condition."
A cordon around the scene of the duo's discovery remained in place yesterday evening as police appealed for any witnesses to come forward.
A woman who saw them slumped on the bench told the BBC they "looked so out of it".
Skripal was among 14 spies swapped by Moscow and Washington in 2014, in what was their biggest spy swap since the Cold War.
He was flown to Britain, where he had reportedly kept a low profile for the last eight years.
The retired Russian secret service colonel had been convicted and jailed for 13 years in 2006 for betraying Russian intelligence agents to Britain's MI6 secret service.
His purported involvement in Sunday's incident has echoes of Alexander Litvinenko, an ex-Russian spy who died in 2006 after being poisoned with radioactivity in London.