Although the club are refusing the comment on the story, the Echo is reporting that Lee is no longer part of Kenny Dalglish's back-room staff.
Lee rejoined the club in May 2008 as Rafael Benitez's assistant manager and kept the job under Roy Hodgson and Kenny Dalglish's time as caretaker manager.
The former Red is already being linked with a quick return to coaching as part of Sam Allardyce's coaching team at West Ham.