Hansen took his case to the Switzerland-based Court of Arbitration for Sport seeking to overturn an International Equestrian Federation (FEI) ruling which disqualifies him from the Beijing Olympics.
If Hansen fails in his appeal, Norway is expected to lose its bronze team jumping medal. If that happens, Switzerland would step up to the bronze position, with The Netherlands fourth.
Hansen's horse, Camiro, tested positive for the banned substance capsaicin, derived from chili peppers.
The hearing was to conclude today (NZ time).
The court is expected to reserve its decision.