The Turf Club said that, following an internal review, the registrar of the Irish National Hunt Steeplechase Committee was asking the appeals body to review the findings of the referrals committee "on the grounds that it was unduly lenient".
Footage appeared to show the jockey striking Kings Dolly at a practice flight before the Flynn Hotel Group Mares Handicap Hurdle on August 18.
The incident was fully investigated and a referrals committee issued the rider with a caution at a disciplinary hearing on Saturday.
Gold Cup-winning rider Russell argued that he wanted the horse to concentrate and that it was inappropriate to use the whip under the circumstances.
But the rider's actions have been heavily criticised in many quarters, including by the RSPCA, who argued that Russell deserved a stiffer penalty.