The 35-year-old centre-half walked out on League two outfit Notts County in September having played only one game in a five-year deal, and he is hoping to resolve his contract dispute with the club at a Football League tribunal.
Campbell, who is currently training with Arsenal, blamed broken promises for his Meadow Lane walkout, but admitted he would be interested in a move to St James' Park.
"I have been approached by several clubs and, yes, it is correct to say that Newcastle are one of them," he said.
"People might be surprised to hear me say that I would be very interested in a move there, but I have my reasons.
"Also, Newcastle are a big club and could be heading back to the Premier League. It appeals.
"If we can sort it all out at the tribunal I would hope to be playing within weeks from now.
"I am training every day with Arsenal, feel fit, as fit as ever, and now I really need some matches.
"But to sort out the mess at Notts County, a Football League tribunal seems to be the only way out."
Campbell wants County to release him from his contract so he can resume his playing career, although he needs special dispensation from the Football Association and is required to explain his reasons for leaving Meadow Lane.