A shoulder injury picked up on Boxing Day against West Ham rules the German out of Sunday's game against Newcastle and potentially their FA Cup clash with Tottenham
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Wenger told Sky Sports: "I would have loved him here [at Newcastle] but he had a shoulder problem, he fell on his shoulder. He will be out for two-to-three games."
The Germany international will not feature against Cardiff on New Year's Day and is a doubt for his side's FA Cup third-round tie against north London rivals Tottenham but could make his return against Aston Villa on January 13.
Jack Wilshere returned to the starting XI in Ozil's place at St James's Park, joining Theo Walcott and Santi Cazorla in Wenger's attacking midfield trio.