The veteran defender was at Celtic Park as new manager Neil Lennon stepped 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 Clydesdale Bank Premier League, 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 - his contract is up at Pittodrie - is reportedly another target.
It also emerged yesterday that Celtic are expected to open talks today with South Korean World Cup star Cha Du-ri.
The Freiburg right-back, 29, is available on a free and revealed earlier this week that he is flying into Glasgow for a medical for the Parkhead club.
He was quoted as saying: "Tomorrow (Tuesday] I fly to Glasgow to undergo a medical check.
"Then I will take two weeks vacation in South Korea."
If talks are successful, the former Bayer Leverkusen player will join up at Parkhead with international team Ki Sung-yueng ahead of the new SPL season, which kicks off for Celtic with a trip to Inverness on the weekend of 14 August.