Mahmoud Ahmadinejad has caused international outrage by dismissing the Nazi Holocaust as a myth and questioning Israel's right to exist.
Last week Germany's main Jewish leader was quoted as calling the Iranian leader "a second Hitler" who must be kept away from the tournament.
Ahmadinejad has suggested that he might visit the national team, but no specific plans have been announced.
The German government, which is involved in delicate diplomatic efforts to defuse concerns about Iran's nuclear ambitions, has resisted calls to bar Ahmadinejad from the tournament.
However, the head of Germany's Central Council of Jews argued that "anyone who can declare the president of Belarus non grata also can clearly show the oil despot he is not wanted" in the country.
In a guest column for the Bild am Sonntag newspaper, Charlotte Knobloch also expressed concern at the possibility of marches by the German far right in support of Ahmadinejad.
Iran's first World Cup match is
"We have to prevent the enemies of the constitution and the Iranian dictator merging into an explosive anti-Semitic alliance," she wrote.
About 15 supporters of Germany's far-right National Democratic Party, carrying Iranian flags and a few posters of Ahmadinejad, demonstrated briefly on Sunday morning on the edge of Nuremberg's old town.
"It is a shock for me that these fascists are demonstrating for Ahmadinejad, because Ahmadinejad is a crazy guy," said Jaleh Yavari, an Iranian who said she has lived in Switzerland for the past 20 years.
Mohammed Aliabadi, one of Iran's seven vice presidents, was expected at Sunday's Group D match against Mexico.
He is the head of the state's physical education organization, which says he is attending the tournament independently; however, the Central Council of Jews has described his presence as a provocation.
Interior Minister Wolfgang Schaeuble has said that, with no UN or European Union travel ban in place against Iranian officials, Germany would have to accept Ahmadinejad.
He has said the German government would make clear his comments are unacceptable if he comes.