Froome is slated to begin the Giro in Jerusalem, seeking a third successive Grand Tour title after claiming his fourth Tour de France title last July and a first Vuelta a España crown last September.
However, the 32-year-old Team Sky leader returned a positive test for elevated levels of salbutamol en route to winning La Vuelta.
As the asthma medication is a specified substance, he can continue racing.
Froome competed at Tirreno-Adriatico earlier this month, stating his desire for the uncertainty surrounding him to be resolved as soon as possible.
Asked when there would be a verdict in the case, UCI president David Lappartient told Italian newspaper La Gazzetta dello Sport, "I don't know to be honest. I hope as soon as possible.
"I said I hope before the Giro but I don't think so, I'm not sure that will be the case.
"We're still pushing to have the resolution as soon as possible. That'd be good for the rider himself, for his the team, for the (race) organisers, for the UCI.
"We don't want to wait for as long as we can imagine. But this is also a technical case. It's not so simple, so that's why it will take some time."
No specific timescale is set in anti-doping cases and there is regular dialogue as Froome mounts his defence to explain salbutamol levels in his urine at more than twice the legal limit.
Froome's case has been ongoing for more than six months after first being made public last December.
This week's podcast with host Christophe Mallet, analysts Dave McKenzie and Pat Shaw review the past week of Cycling, The Middle East leg, and ask the question, Is Froomey really happy with 10th in Ruta del Sol?