The former England defender confirmed last week he was flattered by the Hoops'interest but that his preference would be to stay at Arsenal.
Campbell, 35, has reportedly been offered another one-year contract by the Gunners, though he has also held talks with interim Celtic boss Neil Lennon.
Waiting game: Sol Campbell is torn over a move to Glasgow giants Celtic
'I've spoken with Neil about moving to Celtic. And I've been impressed with what he had to say,' he said.
'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.'
The defender revealed how Lennon sold Celtic to him and that he would not sign unless he knew who the club's permanent manager will be.
He said: 'Neil impresses me. He's come into the job late in the season and that's never easy. But he's done fantastically well.
Talks: Campbell was left impressed after discussions with interim Celtic boss Neil Lennon (L) but the defender wants to stay put with Arsene Wenger at Arsenal
'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.
'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.
'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.'
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