The Daily Star says Redknapp will move to secure Carroll, 19, on a long contract to keep the talented England Under-19s midfielder out of the clutches of his rivals.
"Harry is fully aware that Tom has huge potential and wants to get a deal sorted as soon as he returns," said a N17 source.
"Tom is very similar to Jack Wilshere. It will only be a matter of time before he gets more games and other clubs will be circling. It's crucial to keep him."