In May, the Spaniard sat out Monaco in order to contest the Indy 500.
Now, rumours are circulating that Alonso could return to the wheel of an Indycar for the American series' finale at the Sonoma road course in California.
However, that would require that he misses Formula 1's popular Singapore night race in mid September.
"It's completely untrue," Brown is quoted as saying by Le Journal de Montreal.
The 2017 F1 calendar emerges from its summer break with the Belgian Grand Prix on August 27.