London's Metropolitan Police said it was examining an allegation of sexual assault against a man in 2005 in the Lambeth area of the city.
The alleged victim came forward on Friday, more than two weeks after another male said he was assaulted by the same man in 2008.
Police would not confirm the identity of the alleged assailant, who was named as Spacey by the Press Association.
The American actor is facing numerous claims of sexual assault and harassment, as part of a broader scandal in Hollywood sparked by allegations against mogul Harvey Weinstein.
Abuse claims against Spacey prompted The Old Vic theatre to launch an investigation into the actor's term as artistic director, between 2004 and 2015, receiving 20 claims of inappropriate behaviour.
The incidents reported to the Lambeth theatre cover a period of 1995 to 2013 and have not been verified, The Old Vic said.
Spacey has been accused of attempting to rape a 15-year-old boy in New York and of making advances on actor Anthony Rapp when the latter was 14 years old, 31 years ago.
In a separate incident, a US woman claimed her 18-year-old son was sexually assaulted by the actor last year.
