Lord Lucan vanished from his family home in London in 1974 following the death of family nanny Sandra Rivett. An inquest found he murdered her.
There has since been speculation and stories about what happened to him.
His son, George Bingham, told the West End Extra newspaper the application would provide "closure".
Sandra Rivett, nanny to the 7th Earl of Lucan's three children, was found murdered at the family home at 46 Lower Belgrave Street in central London on 7 November 1974.
Lord Lucan's car was found abandoned and soaked in blood in Newhaven, East Sussex.
The following year an inquest jury found he murdered her.
Despite the fact Lord Lucan was officially declared dead by the High Court in 1999, there have been reported sightings of him in Australia, Ireland, South Africa and New Zealand, and even claims he lived in India as a hippy called "Jungly Barry".
Mr Bingham, who was a child when his father disappeared, told West End Extra he was applying to the High Court under the Presumption of Death Act, which came into effect a year ago.
He said the 1999 declaration had not proved death "for all purposes" and the new law allowed for a "more complete process".
Mr Bingham previously applied to take his father's title in 1999 but his application was denied by the Lord Chancellor because he was "not satisfied" by his case.
The Presumption of Death Act was the result of a campaign supported by relatives of high-profile missing people including chef Claudia Lawrence, who disappeared in York in 2009, and Manic Street Preachers guitarist Richey Edwards, who went missing in 1995.
The son of the peer Lord Lucan, who disappeared almost 41 years ago, has applied to have his father declared "presumed dead".