George Bingham, 30, says he is satisfied from his own inquiries that his father is dead, according to the Daily Mail.
Lord Lucan disappeared after an intruder broke into the family home in London's Belgravia on the night of 7 November 1974.
Nanny Sandra Rivett was beaten to death with a lead pipe and Lady Lucan was then attacked.
Lucan, who was estranged from his wife, spelled out in letters written before his disappearance that he had been passing and had gone to investigate.
But police believed that he was obsessed with his three children, and having lost a custody battle for them, went to wreak revenge on his wife, but mistook the nanny for her.
His bloodstained car was found later, but there was no trace of the peer.
'New Earl in town'
Many "sightings" of Lucan, who enjoyed gambling and was know as 'Lucky' Lucan, have been reported over the past two decades, but investigations have failed to find him.
Lord Bingham is reported as saying: "If anyone buys the official story then they have to explain why a man who murdered out of obsession for his children has made absolutely no contact with them for 24 years."
He said he was going to assume the title and start calling himself the 8th Earl of Lucan, taking his seat in the Lords.
He slept through the dramatic events in London's Lower Belgrave Street.
And he told the newspaper: "I thought it prudent to alert people that there might be a new Earl of Lucan in town."
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