Campbell is currently training with his former club Arsenal, after ending his spell with Notts County.
County still holds Campbell’s registration, but the 35-year-old is hoping that he will be allowed to join another club, after a Football League hearing in early December.
“It [Newcastle] would be a great move for me,” he told Sky Sports News.
“But who knows – hopefully people will sort things behind the scenes and I will get going and play football, which is all I want to do.”
“I am training at Arsenal and keeping fit, which is the main thing and that is fantastic,” he continued.
“I needed to train somewhere, Arsene [Wenger] has done me a great favour and you can’t do any better than Arsenal.”