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Fortune's agent Francis Martin praised Celtic for the way the club dealt with negotiations.
He said: "I spoke to Peter Lawwell this morning and he said, because of Quinton's injury history, Celtic could only offer him a one-year deal.
"Celtic had some concerns about his scans, but it was more to do with his injury record.
"However, Quinton did not want to uproot his family and bring them to Scotland just for one year.
"He is the type of person who would move lock, stock and barrel to a new club, not go somewhere and stay in rented accommodation.
"So he wants to stay in the north-west and will probably sign for Manchester City or Bolton.
"Peter said Celtic will see how he goes in the next season.
"All the clubs have offered much the same and, if other interested parties had offered Quinton three or four years, then Celtic's 12-month offer would have been a concern for us.
"But we understand Celtic have to be sure about a player and it is just one of those things.
"I would like to thank Celtic for the way they conducted themselves - they could not have been more accommodating."