Campbell, 35, is keen to remain at Arsenal and has 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. A switch to Parkhead could appeal should things not work out with the Gunners, with suggestions yesterday claiming Celtic are set to make a surprise summer swoop.
“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.
“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, Hull would consider letting record signing Bullard join Celtic on loan if the Clydesdale Bank Premier League side made an approach.
Head of football operations Adam Pearson said: “We are aware that Celtic have an interest in Jimmy Bullard.
“Everyone is aware of our financial predicament and we would have to consider all offers. If Celtic were to make an offer for Jimmy Bullard, whether it be a permanent transfer or a loan deal, then it is something we have to give serious consideration to.”
Celtic interim manager Neil Lennon said: “I’ve been looking for players but whether the club take any notice of that is another thing.”
He also admits he is still in the dark over his own Celtic future and has no idea when he can expect to find out if he will be the club’s next permanent manager.
He said: “In terms of the job, it is still an ongoing process. It’s just as we were after the Hearts game. The club is going through the technicalities and there are applicants for it.
“I will be around for the next couple of weeks. In early June, I’ll go for the residential part of the ProLicense and the club visit. Then I’m going for three weeks’ holiday.
“There is no guarantee I will have an answer by then.”