The Sun says the striker's latest flare-up came when he stormed out of the club's Melwood training ground yesterday following a disagreement with Benitez over Friday's Twitter revelations.
Babel had outraged the Reds manager by announcing to the world he had been left out of the squad to face Stoke the following day.
Yesterday, Benitez hauled the star into his office to demand an explanation and dish out a dressing down.
But the player hit back by accusing Benitez of ignoring calls from his agent, Winnie Haatrecht, to discuss a move.
Babel was told that was being handled by Liverpool's chief scout Eduardo Macia and that he should concentrate merely on playing and trying to get back into the team. It sparked an angry response from the forward, who took it to mean he was not wanted and raced away from Melwood.
He returned after half an hour, following a telephone call, and Benitez will now hit the Dutchman in the pocket with a fine of two weeks' wages.
The set-to is the most serious in a host of controversies surrounding Babel. He had to explain himself to Benitez after claiming in September the manager had broken promises to play him more.