The well-respected boss questioned the attitude of his players during an angry post-match rant in the away dressing room at Anfield.
Ancelotti is said to have lost patience with several first-team players including midfielder Sigurdsson.
It's claimed that the £45million midfielder could be sold this month, with Ancelotti identifying the player as a lost cause at Goodison Park.
Also facing an uncertain future is goalkeeper Jordan Pickford, who has endured a tricky start to the campaign.
It is claimed that Ancelotti is keen to sign a goalkeeper in the January transfer window to rival Pickford.