The 35-year-old has also reportedly been offered a new one-year deal at Arsenal, but is yet to decide on his future.
Campbell has held talks with interim Celtic boss Neil Lennon.
“I’ve spoken with Neil about moving to Celtic. And I’ve been impressed with what he had to say,” Campbell told the Scottish Sun.
“We’re talking, although we haven’t yet discussed figures. Nothing is set in stone.”
He added: “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.”
