"Rangers have been in for Adam, but I have no interest in letting him go to Scotland," said Southgate in the Sunday Sun.
"Adam can only move during the window and that does not work for us, so he won't be going there. We've had enquiries from 12 Championship clubs for him as well and he might go to one of them.
"He needs to be playing football, it's understandable he's frustrated, but he has to embrace the challenge. He is a rare talent."