The Daily Telegraph leads with the death of Mr Glushkov, who was the right-hand man of Boris Berezovsky, once Vladimir Putin's fiercest rival, who died in 2013.
The Glushkov murder further heightens already tense diplomatic relations between Britain and Russia since the Skripals were found slumped on a bench in Salisbury after being poisoned by a deadly Russian-made nerve agent.
Mr Glushkov was found dead at his home in New Malden, southwest London, on Monday evening.
The Times also leads on Moscow's warning to Mrs May against trying to intimidate Russian Federation, as the PM is expected to tell MPs of plans to retaliate for the use of the nerve agent in Salisbury.
Counterterrorism detectives are leading the case "because of the associations Mr. Glushkov is believed to have had", the Metropolitan Police force said. Police said there was no link at this stage to the attempted murders of Sergei Skripal and his daughter, Yulia.
Police are appealing for any information that could help the investigation into Mr Glushkov's death.
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Glushkov was known to be close friends with Russian businessman Boris Berezovsky, who fled from Russian to the U.K.in the late 1990s after a falling out with Russian President Putin.
Police are reportedly contacting a number of Russian exiles in the United Kingdom to discuss their safety less than a day after the police opened a murder investigation into the death of exiled Russian businessman Nikolai Glushkov.
Mr Glushkov, a former deputy director of Russian state airline Aeroflot was jailed in Russia in 1999 for five years after being charged with fraud and money laundering.
Russian media reported that Glushkov was granted political asylum in Britain in 2010.
In 2017, during a trial in absentia in Russia, Glushkov was sentenced to eight years in prison for allegedly stealing 123 million United States dollars from Aeroflot.
Britains police and security services are making contact with Russians living in exile in the United Kingdom over their safety after the murder of a Russian businessman at his London home earlier this week.
It said Russian Federation had sought his extradition in 2015 "for committing a number of severe financial offences on the territory of Russian Federation", but the British government refused.