In a conference call on Friday, the president of the Austrian Central Bank, Claus Raidl, said Hofer's putative success was "not flattering for us, to say the least."
He added that Hofer's Freedom Party had failed to distance itself from the Nazi rule of Austria from 1938 to 1945.
"In Austria … we have the burden of the past and this Freedom Party … never really drew a red line through the past," Raidl said.
Hofer, who worked as an aeronautical engineer before turning to politics, has struck a more pragmatic line as party leader compared to his polarizing predecessor, Heinz Christian Strache. This may have helped Hofer make inroads in more centrist constituencies.
The presidential role is a largely symbolic one in Austria, with the main leadership coming from the chancellor. Werner Faymann of the Social Democratic Party resigned from this role last week, after his popularity was hit by his handling of the refugee issue. He has been succeeded by Christian Kern.
"He (the president) is more of a figurehead," Raidl said.
"The chancellor is not the boss of president, but the president is also not the boss of the chancellor … He cannot dissolve parliament … the only thing he can do, but this has never been done, he can dismiss the chancellor and the government…. I think (this) will never happen," he added later.