The Senegal striker, who is a practising Muslim, is refusing to wear money-lending company Wonga's logo on religious grounds.
The 28-year-old has told club officials that he is not prepared to promote the company but did offer to wear an unbranded shirt or one bearing a charity logo instead.
According to BBC Sport, sources describe the relationship between Cisse and the club as "strained", with the player's future cast into doubt.
His teammates Moussa Sissoko and Cheick Tiote are also Muslim but they have told the club that they have no issue with wearing the Wonga logo.
Cisse returned to the club later than the majority of the squad having been on international duty with Senegal, and will continue to train on his own until a solution can be found between his representatives and Newcastle club officials.