The 29-year-old joined Stoke in a £5.5million deal in July 2008 but has struggled to win a regular place and was loaned back to Reading for the end of last season.
He said: "Celtic is a club that I have always admired and hoped to get the chance to play for them at some point.
"I have just come back from being on loan at Middlesbrough, where Gordon Strachan is the manager, and he only has fantastic things to say about Celtic, including how unbelievable the fans are.
"Obviously Stoke would need to be happy with any deal, but moving to Celtic would be a great opportunity.
"I am at a critical point in my career when I should be at my peak and I need to be playing.
"And, unfortunately, it doesn't look like I'm going to play too much at Stoke."
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