Matthew Rowley told BBC News that his 45-year-old brother Charlie, who is conscious but seriously ill in hospital, told him he had picked up the perfume bottle. Contacted by AFP, the police refused to confirm the claim.
The police previously said that they found the Soviet-era nerve agent in a "small bottle" in Charlie Rowley's home in Amesbury, near the city of Salisbury in southwest England.
Police said the two had been exposed to a "high dose" of the substance and had handled a contaminated object.
Local MP John Glen told BBC radio earlier that the couple may have come across the object because of their "habit of looking into bins".
Sturgess was living in a homeless hostel in the city.
Britain blamed Russia for the attack against Skripal, a former colonel in military intelligence who was jailed for betraying Russian agents to Britain's MI6 security service.
He left Russia for England in a 2010 spy swap.
Russia has strongly denied poisoning the Skripals, sparking a diplomatic row that has led to tit-for-tat diplomatic expulsions between Britain and its allies and Russia.
Police have not been able to establish whether the Novichok that Rowley and Sturgess were exposed to was from the same batch used against the Skripals but have said that a possible connection is their main line of inquiry.
Sturgess's son Ewan Hope, 19, has called on US President Donald Trump to raise his mother's death at his summit with Russian President Vladimir Putin on Monday.
"We need to get justice for my mum," he said.(
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)