O'Donnell was suspended for 11 weeks on a striking charge.
The matter will be referred to NRL judiciary chairman Judge Greg Woods, who will receive formal submissions from both the Tigers and judiciary commissioner Jim Hall next week.
The submissions will be made privately after which it will be a matter for the judge to decide whether leave to appeal should be granted.
O'Donnell was suspended after a tackle that left Canberra's Michael Monaghan with a double break of his jaw.
Monaghan was initially expected to miss up to three months but could be back in two after successful surgery last week. Judiciary commissioner Jim Hall argued at the original hearing that the seriousness of the injury should be taken into account when the panel decided on its punishment.