The 21-year-old playmaker has been one of the standout performers in Germany's impressive march to the semi-finals in South Africa.
Spanish giants Barcelona and several Premier League clubs, including Chelsea and Manchester City, are reported to be interested in signing the former under-21 international.
However, manager Klaus Allofs has denied reports that the Bundesliga club have already started to fend off official interest from suitors.
"Mesut had appeared in the focus of clubs before the World Cup had kicked off," he said. “Now he is playing a fantastic World Cup campaign, this is definitely increasing interest.
"But when it comes down to concrete bids, nothing has been done. We want him to stay on and actually there is no news. There are no indications he does not want to see out his contract at our club."
Ozil has scored one goal in five World Cup appearances for Germany in South Africa.