The 35-year-old has been at Emirates Stadium since January after Arsene Wenger gave him a short-term contract after his highly publicised move to Notts County ended after one game.
Campbell proved his critics wrong, playing 14 games for the Gunners, but despite being offered another one year contract by Wenger, he could be on his way to Glasgow following talks with interim Celtic manager Neil Lennon.
"I've spoken with Neil about moving to Celtic and I've been impressed with what he had to say," Campbell said in the Scottish Sun.
"We're talking, although we haven't yet discussed figures. Nothing is set in stone.
"I know Celtic are a massive club. I have to consider them. You can't ignore it when such a fantastic club makes their interest known. Neil impresses me. He's come into the job late in the season and that's never easy. But he's done fantastically well.
"Neil told me he's looking for me to be a figurehead in the team. He's made it clear he's looking for more leaders all over the team."
Lennon has been in temporary charge of the Hoops since March after Tony Mowbray was sacked and Campbell believes it's important to know who's in charge first.
"I know he's not yet been confirmed as manager, although there is an expectation he will be. Who knows what will happen? But, yes, it's important for me to know who the manager will be," Campbell continued.
"Neil clearly understands what's needed at Celtic and I appreciate his interest. But we've still got to properly negotiate and the figures might not stack up.
"Celtic is a serious possibility, but I am also talking to a few other clubs. I'm also giving Arsenal the respect they deserve.
"If the situation at Arsenal doesn't resolve itself I know how interested Celtic are and, yes, I'm seriously considering it."
By Owen Edwards
