The veteran defender has been at Celtic Park on Tuesday as Hoops boss Neil Lennon steps up his efforts to recruit the 35-year-old.
Campbell spent five years at Arsenal and impressed during his second spell with the Gunners after returning on a short-term deal in January.
He is now a free agent and Celtic are reportedly set to offer him a two-year deal to make the switch to the SPL, a move he has so far refused to rule out.
Speaking earlier this month, Campbell said: "Football's very important to me and I would give Celtic everything if I sign."
Lennon is keen to strengthen his squad after being handed the manager's job on a permanent basis, following a successful spell as caretaker boss in the wake of Tony Mowbray's departure.
As well as Campbell, he has also been linked with a loan move for Hull City's Jimmy Bullard, while former Aberdeen defender Charlie Mulgrew is reportedly another target.