Sources said 57-year-old Lee had been told by Southgate and Dan Ashworth, the FA's technical director, that his services are no longer required.
Former Italy international Gianfranco Zola says it's only a matter of time before Mario Balotelli returns to the Azzurri setup.
About Rooney, Southgate said it would be "difficult to read any riot acts three months after something has happened."
New England manager Gareth Southgate has hinted he may allow Marcus Rashford to play at next summer's European Under-21 Championship.
Gareth Southgate has confirmed there is no break clause in his four-year England contract and said Wayne Rooney will remain captain of the team.
England have appointed manager Gareth Southgate and here are five key questions he must find an answer to.