The striker, who has confirmed he will be leaving relegated Sunderland, says he has "been blessed" to have been part of the six-year-old's life.
Bradley's parents have said the youngster has just weeks to live.
He suffers from neuroblastoma and is receiving palliative care at home in Blackhall Colliery, County Durham.
Listen: â€œMy relationship with Bradley Lowery was the highlight of my seasonâ€
Footballer Jermain Defoe intends to spend "as much time as possible" with terminally-ill Bradley Lowery after his move to Bournemouth.