The Proton Therapy Centre (PTC) said its experts had studied five-year-old Ashya's medical records and thought he was suitable for the costly procedure.
The news came as Ashya was reunited with his mum and dad, Naghemeh and Brett King, after they were released from jail.
The couple were held in a Madrid prison after taking Ashya from a hospital in Southampton against medical advice.
They were released after UK prosecutors withdrew a European arrest warrant.
Ashya's dad Brett spoke of the family's joy as they were reunited with their son at the Spanish hospital where he is being treated.
Brett said Ashya was 'so happy' and 'so pleased to see us'.
He said: "He couldn't breathe he was so happy. He was so pleased to see us. We're trying to be hopeful."
Following the couple's release from Madrid's Soto Del Real jail, Brett said: "They arrested us and directly they took my son away and said he was not allowed to have any visitors.
"We want to help our son get through this bad time because he hasn't got too many months to live and we're locked away in a cell - we're just trying to speed things up to help him."
He added: "All I could do was just cry and pray. What could I do in a prison cell? I could not do much, really.
"I just want to wet [Ashya's] mouth because he can't drink through his mouth, I want to brush his teeth, I want to turn him side to side every 15 minutes because he can't move.
"I just want to do all those things I was doing from Southampton, I want to do it for him here."
Asked how angry the couple were, Brett said: "My heart is aching for my son and anger can't come in at the moment because I've just got these feelings that I've got to see my son's face."
In the latest development, the Department of Health has indicated that the NHS could agree to fund Ashya's treatment.
It has offered to fly a senior cancer specialist to Spain to assess Ashya, although on Wednesday officials said the offer had yet to be taken up by the Kings.
Mr and Mrs King want their five-year-old son to have proton therapy because they fear conventional radiotherapy could cause him unnecessary harm.
On Wednesday, Iva Tatounova, director of strategy at the Proton Therapy Clinic, said she had informed the Kings that the clinic's team of doctors had reviewed Ashya's notes and confirmed that he was a suitable candidate for the treatment.
She warned that anyone diagnosed with cancer 'should be treated as soon as possible'.
Surgeons at Southampton General Hospital successfully removed Ashya's tumour on July 24 and the hospital was planning to carry out a combination of radiotherapy and chemotherapy to prevent it from returning.
The Kings said they wished Ashya to undergo proton radiotherapy instead of standard radiotherapy.
The treatment is popular because it has a lower risk of side effects, though others are concerned that the long-term impact of the procedure is not yet known.
Although the NHS does not have facilities to treat brain cancer with proton therapy in the UK, last year it provided funding for more than 100 patients to receive the treatment abroad.
However doctors at Southampton refused to refer Ashya for the treatment, saying it would not benefit him more than conventional radiotherapy.
Ms Tatounova said Southampton hospital had now agreed to refer Ashya to the Prague clinic if he first had two courses of chemotherapy.
She indicated that the chemotherapy could be undertaken in Spain or in the UK. The final decision now rests with the Kings, she added.
The Kids'n'CancerUK charity said it had been inundated with donations from the public for the treatment.
By Wednesday night it had received around £41,000, with no sign of the contributions stopping.
Mike Hyman, charity chief executive, said: "I have spoken to Ashya's brother, Naveed, and he is dead chuffed."
The charity believes it will cost £150,000 to pay for Ashya's radiotherapy and associated living costs.
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