The Gelsenkirchen-born midfielder recently completed a switch to the Gunners in a transfer worth €47 million (£40m), and Kahn feels the deal was only possible because Carlo Ancelotti saw no future for the 24-year-old at the Bernabeu.
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"Last season, he only scored nine goals in La Liga - in his position, behind the attackers, this is not enough. Especially if you consider that it's normal for Real Madrid to score a combined 100 goals per season.
"Those who want to survive at a club like Real must prove themselves in every match and show that they're the best of the best.
"It will be interesting to watch if Ozil can prevail in the English Premier League with his filigree way of playing."
Ozil scored 19 goals during 104 appearances for los Blancos since his arrival in 2010. For his country, the German with Turkish ancestry was able to mark 14 times in a total of 47 outings.
However, the arrival of Gareth Bale for a world-record £85 million fee on Monday has made competition for attacking places even tougher in Ancelotti's side.