King's House School on Leagrave High Street offers a private education for children aged between 4 and 11.
Now, it is consulting with families about introducing a new 11+ grammar school option - starting with a year 7 age group in September 2021.
The school is proposing to resurrect its old moniker 'Moorlands' as the name of the facility - which would be the only grammar school in the borough.
A King's House spokesman said: "As a result of demand from parents, we are offering a brand new choice for pupils leaving primary school this coming summer and moving into secondary education in September 2021.
"We are therefore resurrecting the Moorlands name for this new venture. ‘Moorlands’ is the trade-marked name we used between 1926 and 2011 and which still has a resonance in the Luton community in the field of private education."
The school is still consulting with parents about the potential number of pupils in the new school, but class sizes are expected to be kept at around 15 students.
For further information or to request an information pack, visit https://kingshousemoorlands.com/.