The 26-year-old midfielder was suspended indefinitely by the club in the wake of his return to the team in Sunday's 3-0 Barclays Premier League defeat at Liverpool.
Manager Alan Shearer was furious with Barton after he was sent off late in the game for a dreadful tackle on Xabi Alonso, which earned him a three-match ban and ended his season prematurely. There are rumours the pair clashed angrily in the dressing room afterwards, and it is understood the Magpies will do all they can to offload the player in the summer whatever happens over the next few weeks.
If Sunday does prove to be the final straw for Newcastle, Anderson believes £5.8million signing Barton has made his own bed. He said: "A lot of fans didn't want him in the first place, but people were prepared to give him a chance.
"Everybody deserves a second chance - but you just wonder how many chances this guy actually wants. Sam Allardyce brought him in because he thought he could control him and change his temperament.
"But when you are like that, you are never going to change. It's just in his nature, it's in his make-up and there's not a great deal you can do about it. He kept coming out with statements that he was going to change his ways, but Sunday just proved he hasn't changed at all."