The 26-year-old was pictured taking a selfie with a red and black snapback cap along with the caption, “The #Singapore skyline is simply awesome.”
Özil joined Arsenal two summers ago from Real Madrid for a record £42.5 million transfer fee and has been in top form in recent months following a lengthy spell on the sidelines due to an injury.
The former Real Madrid star has won two Vitality Arsenal Player of the Month and a PFA Fans Player of the Month award since the turn of the year.
The World Cup winner provided nine assists and five goals in 32 appearances for Arsenal in all competitions last season.
Özil spent his summer holiday in Los Angeles but has since returned to Arsenal for pre-season training and is expected to remain at the club next season.