On Thursday, police raided Glaeseker's home as part of an investigation into corruption allegations.
Media reports claimed the former spokesman supported a series of events organised by Manfred Schmidt, an event manager closely connected to the president, between 2007 and 2009.
In return, Glaesker was allegedly given several holidays in Schmidt's properties.
The Bild am Sonntag newspaper claimed the perks did not stop there. The paper reported Saturday that Glaeseker received free air travel at least five times over the past year, while he was working for President Wulff.
Glaeseker reportedly used Schmidt's VIP card with carrier Air Berlin to travel to Turkey and Mallorca.
Schmidt's offices in Berlin and Switzerland were also raided on Thursday, with police removing computers and documents.
Wulff fired Glaeseker, the man often described as his closest advisor, in late December without publicly stating a reason.
Prosecutors said they were not investigating Wulff on suspicion of criminal activity.
A new opinion poll by the Infratest dimap shows less than one-third of all Germans still view the president as trustworthy, amid the controversy surrounding a €500,000 home loan Wulff borrowed from the wife of a businessman friend while state premier of Lower Saxony in 2008, and failed to declare.