Siegler takes on the role on an interim basis, alongside his existing responsibility as spokesman to FIFA president Sepp Blatter.
Cooper was fired this week after seven years as FIFA's communications director.
The body declined to give reasons for the decision, but a statement was expected after PRWeek went to press.
Speculation suggests Cooper's departure comes as part of a staff clear-out led by Blatter, which has already seen the former general-secretary Michel Zen-Ruffinen depart.
Cooper said, in a statement, he had been given no explanation for his dismissal: 'This is something of a surprise coming less than two weeks after the end of a World Cup in which the media organisation was regarded as one of the best of its kind.'
Siegler will continue in the comms director role until an executive committee meeting in September, when a group restructure will be proposed.