The five-year-old's parents Gemma and Carl have met with staff at Great Ormond Street Hospital in London to discuss if he should be given a place on the programme.
The CAR T cell trial is funded by Cancer Research UK and while it is in its early stages, it has been shown to help those with other forms of cancer.
Bradley, from Blackhall Colliery, has beaten neuroblastoma once before, but doctors found it had returned last summer and despite gruelling treatment his tumours have grown.
Specialists at Newcastle's Royal Victoria Infirmary have told his parents they have just time to spend with their boy, who has gained a huge following of support after appearing as a mascot at Sunderland, Everton and England games.
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A charity fund to help cover the cost of treatment has already raised £700,000, with part of it used to cover the cost of antibody treatment, which started here in the North East in January.
Tonight, Gemma issued an update about the plans being made to hopefully give her son a better chance.
She said: "Myself and my husband had a meeting with the medical staff yesterday at Great Ormond Street about the new trial that Bradley has been accepted on.
"It must be made clear to everyone that the trial is only phase one.
"This means that it is in very early stages and can not be deemed as a miracle cure.
"There is no evidence yet to say it will work, there is a high possibility it won't work.
"No decision has been made yet if Bradley will go on this trial as it will all depend on the scan results on Friday and other tests to see if Bradley is strong enough.
"Thank you for your continued support."
More details about Bradley's appeal can be found via the Facebook page Bradley Lowery's Fight Against Neuroblastoma.