Jack Wilshere vacated the number when he left on loan for Bournemouth.
"It just went free, and I definitely want it," said Ozil when he was asked about the Arsenal No 10 shirt in an interview with German newspaper Express.
Ozil said the number meant a lot to him, as it put him in a lineage of sorts.
"It's my favourite number. Football legends like Zinedine Zidane, Diego Maradona and Pele wore that number on their backs. I'm really very happy to have it."