The Germany international was initially expected to be out for three months, but manager Arsene Wenger remained hopeful he would be ready to return before the end of 2014.
However, Ozil thinks he is unlikely to be back for another seven weeks, meaning he looks set to be sidelined until the new year.
"I have already been out for five weeks and will be out for another seven weeks," he said at the Laureus World Sports Awards.
"That is a really long time but that is the way it is in football sometimes.
"My head is held high and we look forward."
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