Froome is currently cooperating with the UCI in the matter, which he says is not an anti-doping rule violation. The Team Sky rider has long used the drug to control his asthma.
Under UCI rules, cases like Froome's would not be made public unless they resulted in a rule violation. But the information was leaked to the press earlier this month, leading to a media storm that could drag out well into next season - a situation Prudhomme wishes to avoid.
"We want the situation to be cleared up, to get out of the darkness and ambiguity," Prudhomme told France Info TV on Friday. "We obviously want an investigation to be conducted, and we don't want it to last for months and months, so we can have an answer from the UCI as soon as possible next season."
Because athletes vary widely in their metabolism of the drug, WADA rules allow athletes who test over the threshold limit to undergo a controlled study to attempt to demonstrate that the levels were not the result of an anti-doping rule violation, such as taking more of the allowed dose of 800 micrograms over 12 hours or 1,600mcg in 24 hours, or using a prohibited oral or injection delivery route.
One of Froome's urine samples from the Vuelta a España tested at twice the allowed WADA limit for the asthma drug. Because of the anti-doping rules surrounding the so-called "specified substances", Froome is not subject to a provisional suspension while his case is under examination.
"Salbutamol is not a banned substance," Prudhomme said. "What matters is the amount taken, that's why an expert battle will take place, although it looks like the dose found was twice the permitted level."
Froome faces the possible loss of his Vuelta a España title and a ban, most likely back-dated to his date of notification on September 20, 2017. In past cases, riders have been given bans of nine months to a year after similar AAFs.
Froome has denied any wrongdoing, and said he increased his dose of salbutamol under the recommendation of the team doctor after his symptoms worsened during the Vuelta.