Matthew Rowley said his brother Charlie, who is conscious but seriously ill after he was exposed to the poison, told him he picked up the container.
Salisbury MP John Glen told BBC radio the couple may have come into contact with the bottle because of their “habit of looking into bins”.
Police have not confirmed the claim.
Charlie Rowley, from Amesbury, Wiltshire, fell ill on 30 June hours after his partner Dawn Sturgess, 44, collapsed after being exposed to novichok.
Ms Sturgess, who lived in a homeless hostel, died on 8 July.
Police said the couple had been exposed to a “high dose” of the substance after handling a contaminated object, and the nerve agent was found in a “small bottle” in Mr Rowley’s home.
Amesbury is close to the city of Salisbury where the former Russian spy Sergei Skripal and his daughter Yulia were targeted with novichok on 4 March.
The government has blamed the attack on Moscow.
Mr Skripal and his daughter were found unconscious on a bench in Salisbury after the poisoning, but have both since recovered.
Ms Sturgess’ teenage son Ewan Hope has called on the US President Donald Trump to raise the issue with Russian President Vladimir Putin during their summit in Helsinki.
The 19-year-old told the Sunday Mirror: “I don’t share Donald Trump’s politics and I’ll never be a supporter of his, but I would like him to raise mum’s case with the Russian president.
“We need to get justice for my mum.”
Police have not been able to establish whether the novichok that Mr Rowley and Ms Sturgess were exposed to was from the same batch used against the Skripals.
They have said that a possible connection is their main line of inquiry.
More than 400 exhibits, samples and items have been recovered by police investigating the poisoning of Mr Rowley and Ms Sturgess.
Russia has strongly denied poisoning the Skripals, sparking a row that has led to tit-for-tat diplomatic expulsions between Britain and its allies and Russia.