British authorities seized the unlicensed products, which included steroidal injections, anaesthetics and anti-inflammatories, from a Dubai government private jet at London's Stansted airport earlier this year, according to the report.
Sheikh Mohammed bin Rashid Al Maktoum is believed to have asked Princess Haya, his junior wife, to conduct an internal investigation into the seizure.
The monarch is Britain's leading racehorse owner and runs Godolphin Racing, the Maktoum family's private thoroughbred horseracing stable.
The BHA said there was no evidence that anyone other than Al Zarooni was involved in the case at the Gulf outfit's stables in Newmarket, eastern England.
Al Zarooni was suspended and later banned.