The 2018 and 2022 World Cup will be played in Russian Federation and Qatar respectively, while the 2026 and 2030 tournaments have not yet been awarded.
The proceedings relate to the sale of World Cup TV rights to BeIn Sports, where Al-Khelaifi is chief executive, and are connected to the ongoing investigation into former Federation Internationale de Football Association secretary general Jerome Valcke.
The Guardian has approached representatives for Khelaifi and Valcke for comment. In January 2011, Federation Internationale de Football Association announced that al Jazeera Sports - which later became BeIN - secured the rights for 23 territories across the Middle East and North Africa, including Saudi Arabia.
The statement from Switzerland's top prosecutor also alleges illegal dealings with "Nasser Al-Khelaifi in connection with the award of media rights for certain countries at the FIFA World Cups in 2026 and 2030".
Nasser Al-Khelaifi, the Qatari president of Paris Saint-Germain, is facing criminal proceedings in Switzerland in connection with the award of media rights for certain countries at the FIFA World Cup.
Findings obtained in that process have led to a separate line of inquiry involving PSG president Al-Khelaifi. He became the chairman and chief executive officer of the French club, who broke the world transfer record to sign Neymar earlier this year, four months later. BeIN has also acquired a broad portfolio of rights including from European soccer body UEFA for the Champions League and national team matches.
Valcke was banned from football for 12 years, later reduced to 10, by Fifa's ethics committee in February last year for seven breaches of the organisation's ethics code, including attempting to sell TV rights for the 2018 and 2022 tournaments for "far below their actual value".
"The company will fully co-operated with the authorities and is confident as to the future development of this investigation". The DoJ has indicted or secured guilty pleas from more than 40 people.