A cancer charity in Derby said the King family have accepted their offer to pay the full cost of the proton beam treatment for five-year-old Ashya.
Kidsncancer chief executive Mike Hyman told ITV News they have been inundated with donations from the public following the arrest of Brett and Naghmeh King. He said:
It will take at least a £100,000, and probably a £150,000 to pay for the treatment as well as the cost of accomodation for the months of the treatment for the family. It is our wish that they come back from wherever they go they are not in debt, and can return to their normal life.
The situation they have been through is absolutely appalling. To be imprisoned like criminals, 300 miles away from their sick child is disgraceful and disgusting.
I have been overwhelmed by the generosity of the public, who obviously feel like we do that this family deserve support at this desperate time.
The donation page set up by the charity has made almost £24,000 so far.
Ashya King's parents told the Daily Mail they fled the UK after being told NHS treatments would leave him with life-long disabilities.
The head of the police force which applied for a European Arrest warrant against the parents of Ashya King has now urged their release.
A British mother whose son's life was saved by proton therapy has told ITV that she defied NHS doctors' advice to pursue the treatment.