The Swede is currently caretaker manager after Unai Emery's sacking yesterday.
The Guardian says Ljungberg will be also be able to audition for the role until the end of the season.
Ljungberg is desperate to impress and wants the job on a full-time basis.
But the Swede is under no illusions of the task he faces and expects no favours from another Invincible, technical director Edu.
He is well respected at the club having impressed in a variety of roles, from the under-15s, the under-23s and as a first-team coach.