Bradley, who celebrated his sixth birthday this week, has been battling neuroblastoma, with his fight touching the hearts of people around the world. Groups across Yorkshire have been raising funds for the inspirational boy.
He has appeared as Sunderland's mascot several times this year, as well as for Everton, and in Defoe's England comeback match at Wembley in which he scored.
Northumbria Police said they were "made aware" of messages relating to the youngster on Friday.
In a statement, the force said: "A 15-year-old boy has now been interviewed under caution and will be dealt with by the youth offending team."
Bradley, who is from Blackhall, County Durham, celebrated his birthday with his best friend Jermain Defoe and more than 250 family and friends on Friday evening.