Parents last week received a letter from the headteacher and chair of governors outlining proposals for the school to join the City of London Academies Trust by September 2024.
The school has a 109-year history, having been founded in Rotherhithe in the wake of the Titanic disaster. It moved to Broadwall SE1 after World War II, before settling on its current Stamford Street site in 1965.
The front portion of the school building is more than 200 years old, having been built for the Benevolent Society of St Patrick as a school for Irish children.
London Nautical - which received a 'requires improvement' rating at its latest Ofsted inspection - is currently a Lambeth Council maintained school.
"The decision to consider academy conversion is one that has been ongoing for two years," wrote headteacher Michael Schofield in his letter to parents.
"During this time, the governing body and I have met with a range of multi academy trusts (MATs) available for us to join, looking carefully into the benefits and potential drawbacks.
"We have also closely monitored the national, regional, and local education position to ensure that we are able to make the correct decisions when setting the future direction of our school.
"Having carefully considered how any change in status will benefit our school we have identified one MAT, the City of London Academies Trust, that we feel will enhance the educational experience and opportunities provided to students, staff and the community that we serve."
The City of London Academies Trust is sponsored by the City of London Corporation - the Square Mile's local authority.
The trust already includes three Southwark Schools - City of London Academy Southwark in Lynton Road, Galleywall Primary School and Redriff Primary School.
CoLAT currently operates in four boroughs bordering the City of London - Hackney, Islington, Southwark and Newham - and oversees six secondary academies, three primary academies and one sixth form centre.
London Nautical would be the Square Mile's first academy in Lambeth, although the City Corporation is already a social landlord in the area.
Parents have been invited to a meeting about the proposals on 7 February, with a formal consultation period to follow the half term break.