Several tape machines were discovered at a junction box near the north London home Deayton shares with partner Lise Meyer and their 18-month-old son, according to The Guardian newspaper.
They were reportedly planted shortly after the News of the World newspaper said Deayton had taken cocaine and had a "two-night affair" with prostitute Caroline Martin.
The man has been arrested on suspicion of conspiracy to cause criminal damage to BT property and the unlawful interception of communications.
The Guardian said police are investigating claims the man was working for a private detective.
A Scotland Yard spokesman said: "The Metropolitan Police's Specialist Investigations Team arrested a 34-year-old man at a residential address in Hertfordshire.
"He was taken to a north London police station and released on police bail to return at the end of the month."
Deayton has obtained a High Court injunction stopping the Mail on Sunday publishing more details about his private life and medical history.
A spokesman for the newspaper, which is seeking a full hearing to overturn the decision, said: "No telephone engineer has been employed by the Mail on Sunday."
Following the News of the World revelations, Deayton and Ms Meyer flew off to Italy to escape the publicity.
But he returned to face ridicule on his satirical show Have I Got News For You.
Reports Deayton would be replaced by actor Stephen Fry have been denied - but his salary, reportedly £500,000, is under threat, The Guardian says.
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