Detectives revealed that the 68-year-old may have let his killers into his home, while appealing for anyone with information to come forward.
Commander Clarke Jarrett, head of the Metropolitan Police’s counter-terrorism command, said numerous statements had been taken and more than 400 pieces of evidence were being processed.
“We have found no sign of forced entry thus far, but the forensic examination at Mr Glushkov’s home continues and we expect to be there for some time,” he added.
“I must stress that there is nothing we have found in our investigation so far to suggest any link to the attempted murders in Salisbury and I would like to reassure the public in New Malden that there are no wider public health concerns in relation to this investigation.”
Mr Glushkov was found dead at his home in New Malden, south-west London, on Monday evening.
The incident was initially treated as “unexplained” but police announced a murder inquiry on Friday, when a source told The Independent Mr Glushkov may have been strangled with a dog lead.
A post-mortem examination gave the cause of death as compression to the neck and police say they are “retaining an open mind” about the killing.
“I would like to thank the public for their response to our appeal so far and I would urge anybody who may have information to get in touch if they have not already done so,” Commander Jarrett said, as uniformed officers patrolled New Malden.
They are appealing for information from anyone who saw anything suspicious near the victim’s home in Clarence Avenue on March 11 or 12.
Counter-terror police area leaving the investigation as a precaution “because of the associations Mr Glushkov is believed to have had”.
Mr Berezovsky was found hanged in the bathroom of his Berkshire home in 2013.
Police said a post-mortem showed no sign of a violent struggle, and an inquest recorded an open verdict after hearing conflicting evidence.
At the time, Mr Glushkov said he believed his friend had been murdered, telling The Guardian: “I don’t believe Boris died of natural causes. Too many deaths [of Russian exiles] have been happening.”
Mr Berezovsky’s death is among up to 14 being reviewed by police and MI5 in light of the nerve agent attack on Mr Skripal and his daughter in Salisbury.
Mr Glushkov worked for Mr Berezovsky’s LogoVaz car company in Russia, before becoming the first deputy general director for Russia’s flag carrier Aeroflot in the late 1990s.
He served a five-year term for money laundering and fraud in Russia, then fled the country after being handed a two-year suspended sentence for fraud in 2006.
Last year, he was sentenced to eight years imprisonment and a 1 million ruble fine in absentia for allegedly defrauding Aeroflot – a case that continued at the time of his death.
Mr Glushkov, who has two children, was due to attend a commercial court hearing on Monday morning but did not arrive, sparking concerns among friends who later confirmed his death.
His LinkedIn page listed him as a “private consultant” in financial services since 2011.
Police described Mr Glushkov as a “retired financial director” and said he had lived in the home in Clarence Avenue for two years.
His family has been informed of his death and are being supported by family liaison officers.
One of Mr Glushkov’s neighbours, Patricia Egan, described him as a “lovely fellow” who had regular visits from his adult daughter, and an adult son.
She said he had an operation a few months ago on one of his legs for arthritis, adding: “He didn’t go out much because of his illnesses, he had something wrong with his heart and had a few strokes.”
Ms Egan said Mr Glushkov was intelligent, educated, and well-mannered, generous and friendly, noting that he spoke very good English, adding: “He told me he was from Georgia and always said how beautiful it was.”
The murder came almost exactly a week after former Russian double agent Sergei Skripal and his daughter were poisoned with a nerve agent in Salisbury.
They remain in a critical condition in hospital amid an escalating diplomatic row with the Kremlin, which has denied involvement after the Government named a Soviet-era nerve agent as the weapon and announced the expulsion of 23 Russian spies.
Russia’s official Investigations Committee has launched its own criminal investigations into the attempted murder of the Skripals and Mr Glushkov’s death.