Before his rescue and treatment, the tiger was dehydrated, infested with parasites and exhausted, as well as having gastrointestinal, liver and kidney issues, the park said.
In October, Nichols said the park was waiting for vets to check Aleks was healthy enough for the long journey across Europe.
On Friday, he said: “We are at the stage where all we need is the dimensions of the carrying crate for Aleks so a vehicle can be allocated and a date.”
He said the park expected to be given a date “imminently” for when Aleks will be starting his journey across Europe.
“I would say within the next three weeks he will be on the road here,” he added.
Aleks will be driven from Ukraine through Poland and northern Europe and then from Dover to his new home at Lincolnshire Wildlife Park.
When he arrives, Aleks will go through a three-stage process to get him settled – initially in an indoor closure with a sleeping area, playroom and feeding room.
With veterinary help, he will move to an outdoor enclosure before joining other tigers at the park.