The Sun said a man, aged 23 at the time, made a complaint on Tuesday about the alleged incident in the London borough of Lambeth.
The Met confirmed that they are investigating an alleged assault on a man from 2008.
They would not confirm the allegation was made against House of Cards actor Spacey.
Spacey said on 2 November he is seeking treatment after facing allegations of sexual misconduct from a string of men.
No arrests
The Sun reported that a British actor claimed he woke up to find Spacey performing a sex act on him in 2008.
The man is said to have run from the property after Spacey allegedly said: "Don't tell anyone about this."
A spokesman for the Met said it had no record of any arrests having been made in connection with the investigation and police declined to comment on The Sun's report, which says the complainant had been interviewed by police.
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