Brown was acknowledging the rumours that the Spanish driver may not stay in Formula 1 or at McLaren beyond this year.
Alonso, 36, did the Indy 500 last year and is attempting the full world endurance championship plus Le Mans in 2018.
Nevertheless, Brown says McLaren wants Alonso to stay.
"We want him to continue here for many years and we want him to continue at McLaren," he told AS.
McLaren has young charger Lando Norris waiting impatiently in the wings for an opportunity, but Brown said the British team is still focused on Alonso.
"Formula 1 is his passion, but he's been doing it a long time and he's achieved everything. So we'll see," he added.
"But he loves McLaren, the work we do, everything. I don't think he was this happy at another team.
"We'll sit down in the middle of the year and see. He will see how the car develops and the further improvements we are going to bring.
"But I think Fernando's heart is in Formula 1 and at McLaren. He wants to win."
Alonso is seventh in the drivers' standings ahead of next weekend's Monaco Grand Prix.