Keswick talked up the signing of Özil - calling him "one of the world's best players" - but said the club would continue to follow a prudent course.
"It is my job to ensure we steer further along the course we have set," he said. "We must continue to grow commercially to provide the club with the best opportunity to achieve success and we must do this in a way which remains true to our values and which ensures and protects the long-term sustainability of the club."
He underlined, however, that significant sums remained available for Wenger to spend, if he deemed it necessary. "With the Özil transfer I believe we have made a significant statement and when Arsène decides the time is right to invest again Stan Kroenke, myself and the rest of the board will be delighted to support him."