Lundekvam is still hoping a switch to Scotland could happen in January and would walk away from a handsome pay-day on the South Coast to do so.
"There was real interest from Celtic but they had to sell a couple of guys before I could go and that didn't happen," he told the Scottish Sunday Mail.
"I would have been keen to play for them if an offer was accepted but it wasn't to be.
"The fact Celtic are a massive club and Gordon is boss would have been factors in me wanting to go there.
"I know him from his time at Southampton - he did a great job for us. Of course I would consider going to Celtic in January if they still wanted me.
"It's my testimonial year so it would be a hard decision but I would definitely look closely at what they had to offer."
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