The arrests were made in twin pre-dawn raids in the English city of Birmingham on Wednesday.
A witness said a man led away from a Birmingham home resembled one of the four suspects in the 21 July failed bombings, whose photographs have been widely distributed.
Britain's Press Association said detectives believed the man, who was overpowered by police using a stun gun and then taken to London, was one of the would-be bombers.
A spokesman for London's Metropolitan Police declined to confirm or deny British media reports that one of those arrested was wanted as a suspect in last Thursday's attempted bombings.
The spokesman said three of the four arrested in Birmingham were being held by police in the West Midlands while one was being transferred to a London police station, without saying which one.
Another police spokesperson said earlier that three of the four arrested in Birmingham were seized at one address.
"A suspect package has been found and, as a precautionary measure, evacuation has been undertaken in the vicinity," the spokesperson said.
"These operations are in connection with the incidents in London on 21 July."
The spokesperson said officers fired at one man with a Taser gun, a weapon that delivers an electric shock.
The Birmingham arrests bring the number of people that police have said are being held in connection with the 21 July attempted bombings to nine.
Police last week arrested and were questioning five other people in relation to the botched attacks.
Three more held
On Tuesday night, two men were arrested at Grantham railway station under anti-terror laws as they travelled from Newcastle to Kings Cross station in London, but police would not say whether they were linked to London attacks.
The arrests were made after information was given by two off-duty officers from London's Metropolitan Police who were travelling on the same train.
They are to be questioned at a Lincolnshire police station later on Wednesday.
Another man was arrested on Wednesday as he prepared to travel on a flight to the southern French city of Nimes from Luton airport north of London, but it was not immediately known whether he was connected to the 21 July investigation.
The authorities briefly diverted flights from Luton amid a
security alert that turned up to nothing, the police said.
Police are searching for the would-be bombers amid reports they may have re-armed after the 21 July attacks failed to repeat the carnage of the 7 July suicide strikes, which killed 56 people and injured about 700.