Mr Berezovsky was also a friend of Russian dissident Alexander Litvinenko, who was poisoned with radioactive polonium-210 in London in 2006.
The businessman was reportedly found in his London home with the cause of death not yet clear. It did not identify him by name.
A coroner concluded it was impossible to establish whether the oligarch was killed or committed suicide.
London police said its Counter Terrorism Command is leading the investigation "as a precaution because of associations that the man is believed to have had".
But police said there was no evidence to suggest a link to the March 4 poisoning of former spy Sergei Skripal and his daughter.
According to the Russian Embassy in London, the United Kingdom refused to extradite Glushkov in February 2016 on charges of large-scale fraud and embezzlement during his time as the deputy director of the Russian national airline Aeroflot.
EU to respond within 90 days if not exempt By
EU Trade Commissioner Cecilia Malmstroem said the bloc was "not preparing for battle" but had to be ready to protect its industry.
Glushkov, who worked for Berezovsky's LogoVAZ vehicle company, was charged with money laundering and fraud and spent five years in jail from 1999.
He was released in 2004, before he was granted asylum to the UK. In 2011, he gave evidence at the court case brought by Berezovsky against Kremlin-friendly oligarch Roman Abramovich.
Nikolai Glushkov's home in New Malden. Natasha is believed to live in the UK. In 2017, he was convicted by a Russian court in absentia for allegedly defrauding Aeroflot of $122 million while serving as the company's finance director the 1990s.
The White House on Monday condemned the poisoning of the ex-Russian spy in the U.K."The use of a highly lethal nerve agent on U.K. soil is an outrage". They were found unconscious on a bench in Salisbury.
Earlier on Tuesday, Britain's representative to the global chemical weapons watchdog the Executive Council of the Organization for the Prohibition of Chemical Weapons (OPCW), Peter Wilson, lambasted Russian Federation.
The Russian Foreign Ministry, meanwhile, says it has handed the British ambassador a note of protest regarding the accusations, calling them "baseless", "provocative" and "another unscrupulous attempt of the British authorities to discredit Russia".