Lennon is extremely keen to land the Arsenal man, and is reportedly ready to give him a two-year, £35,000-a-week deal, while the Gunners only want to offer a one-year contract.
But Lennon has also told the 35-year-old he can jet off with wife-to-be Fiona straight after their mid-July wedding which means he would also be absent for most of the four-game North American pre-season tour.
Celtic are due to report back for pre-season training on July 1, and likely to fly out to America on the 12th.
They face a crucial Champions League third qualifying round first-leg tie on July 28-29 with the return on August 4-5.
"I'm getting married on July 17," Campbell told the Scottish Sun. "But Neil's told me he's quite flexible, that if I need ten days-two weeks honeymoon then he'll be fine with that.
"That really makes me happy because if I'm not happy, and my family's not happy, then you're not going to play your best football are you?
"If I were to sign for Celtic then I'm likely miss the first leg of the European tie.
"I don't know who Celtic will get, but hopefully it would be someone that would give them a good chance of progressing.
"It's a difficult one, but I can't move my wedding.
"Football's very important to me and I would give Celtic everything if I sign."