Alonso was allowed to miss the Monaco GP earlier this season in order to instead compete in the Indy 500 race in the US.
The switch fulfilled a lifelong ambition for Alonso and there has been speculation he could race again in Indycar in the American series' finale at the Sonoma road course in California.
If he were to appear in that race, the McLaren driver would have to sit out the F1 Singapore night race in mid September.
However, Brown has denied the reports and told Le Journal de Montreal: "It's completely untrue".
Alonso has struggled at McLaren this year, failing to make it onto the podium at all in the 11 races so far, managing just 10 points to sit way off the pace in the Drivers' Standings.