The 27-year-old was removed from the Olympic programme on Thursday when the International Bobsleigh and Skeleton Federation jury ruled that imagery on the helmet - depicting athletes killed since Russia’s invasion of Ukraine - breached rules on political neutrality at the Games.
Heraskevych is seeking reinstatement or at least a CAS-supervised run, pending a decision by sport's highest court ahead of the final two runs set for Friday evening.
CAS secretary general Matthieu Reeb could not say exactly when they were likely to reach a decision despite the tight schedule.
“We hope to have a final decision announced today, but it’s difficult for me to say when," Reeb told reporters. "Obviously, we know the schedule of the competition, and it is an objective for CAS to be able to make a decision before the start of the race, but we don’t know how long the hearing will take.
"We have only one arbitrator from Germany, and she will be in charge of this case. We have participants attending in person, like the IOC, the athlete is here, the father of the athlete is here.
"We have a representative of IBSF attending remotely. The athlete is also assisted by legal counsel speaking from Kyiv."
Heraskevych insisted his place was not in Milan but in Cortina d'Ampezzo, where the sliding competitions are being held.
“I should not be suspended. I believe I did not break any rules,” Heraskevych said.
“I should be part of the Games, part of the competition and not of the hearing.”