McLaren took overall honours in the French endurance classic in 1995, with JJ Lehto, Masanori Sekiya and Yannick Dalmas sharing the winning F1 GTR. Its works program continued until the end of 1997, with McLaren's last appearance coming in 1998.
Brown explained that a return to Le Mans for the Woking marque would fit with his remit of promoting the brand following his appointment as executive director of the McLaren Technology Group, which incorporates the car-making division.
"We have won Le Mans and the race is in our history, and part of my job is to decide where the McLaren brand should race," he told Motorsport.com's sister title Autosport.
"Going back to Le Mans is something we have identified and are discussing. Personally, I would love to see us go to Le Mans, and I'm not the only one with those views."
The ultimate decision on a return to the 24 Hours would be made by McLaren Automotive and chief operations officer Mike Flewitt, Brown stressed.
He said a Le Mans comeback would most likely come in the GTE ranks, but when asked if McLaren could build an LMP1 car in an attempt to repeat its outright triumph, he replied, "never say never".
Brown said that a GTE program involving a World Endurance Championship assault "would take several years to put together".
The comments from Brown come after the appointment of a new head of motorsport in former Strakka team boss Dan Walmsley at McLaren Automotive's special operations division.
Brown said that it was "to be determined" if developing a GTE car would be handled in-house or by McLaren GT, the independent and self-funding company that has produced the manufacturer's GT3 and GT4 machinery since 2011.
McLaren GT boss Andrew Kirkaldy has repeatedly stressed that his company would need the support of McLaren to develop a car for the factory-dominated GTE division, as distinct from its GT3 and GT4 customer programs.
"There have been discussions, but I can't say too much," he said. "The hope is that we would be involved."
McLaren GT has ongoing contracts that cover the life of the 650S GT3 and the 570S GT4 racers.
A GTE version of the MP4/12C GT3 was on the cards in 2012, with development due to start in ’13.
The program was shelved after the FIA and WEC promoter the Automobile Club de l'Ouest launched an ultimately unsuccessful bid to bring the GTE and GT3 regulations together.