The 35-year-old, who was captain of Arsenal's Invincibles 2003/2004 team, impressed after his return to his old club on a short-term deal during January.
A new contract is on offer for the veteran, but has not yet been formally agreed.
Rolling back the years: Campbell (right) has been in fine form for the Gunners
Campbell hopes to be part of Arsene Wenger's squad again next season, which may be without captain Cesc Fabregas who appears set on a move to Barcelona.
However, a switch to Parkhead would appeal should things not work out with the Gunners.
'I worked very hard to get back to my best and to play in the Champions League again, and I would love the opportunity to continue at Arsenal,' Campbell said.
'Although a one-year contract has been offered, these things take some time to thrash out - and I imagine Arsene has quite a lot to deal with at the moment, particularly with Fabregas.'
Campbell added: 'I am in no rush, I would like to stay with Arsenal if I could. However, Celtic are a massive club, a great club, with massive support.'
Meanwhile, the Glasgow outfit are monitoring the situation of Lazio defender Mobido Diakite.
The French centre-half endured a frustrating season in the Italian capital, failing to hold down a starting role despite impressing when given the chance.
The 23-year-old's agent, Ulysses Savini, said: 'He is being followed by teams in the Premier League, Ligue 1, Celtic, Panathiniakos, and Galatasaray.'
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