The 15 year-old has been likened to Manchester City centre-half John Stones and is set to be promoted to the Dons first team.
Carrol turns 16 next month and will be due to sign pro terms in Scotland.
Advertisement
Advertisement
The Athletic says Chelsea and Arsenal are both keen to bring the young Scot to London.
Should he remain on amateur forms this summer, Aberdeen will still be due compensation should he leave.