Under article 28 of its rules ASO "expressly reserves the right to refuse participation in - or to exclude from - the event, a team or any of its members whose presence would be such as to damage the image or reputation of ASO or the event".
Salbutamol is a specified substance rather than a prohibited one, meaning Froome was allowed the chance explain the test result and continue racing in the meantime.
The Brit has been continued to compete despite the ongoing doping case against him and won the Giro D'Italia in May. Five-time Tour victor Bernard Hinault has called on other riders to go on strike if Froome is cleared to compete.
Sky, ASO and the French Olympic Committee will each choose an arbiter to decide whether Froome should be allowed to start the Tour.
UCI president David Lappartient reacted to the story on the sidelines of the French national championships.
Since he didn't get any reply from the sporting authorities since this announcement, Prudhomme expects to see Froome at the start of the Tour on July 7.
Team Sky have yet to unveil their eight-strong team.
He is just the third man to hold all three of cycling's Grand Tour titles at the same time.
But Le Monde commented that "the Tour de France wants to avoid at all costs finding itself in the same situation as at the recent Tour of Italy where Froome's final win is now marked with an asterisk".
Froome's appeal against a drugs test remains unresolved.
Michelle Froome, who also represents the cyclist, said: "Chris will ride the Tour".