Khelaifi, a Qatari with close ties to the Gulf state's royal family, is under investigation for allegedly striking illegal deals with disgraced former Fifa secretary general Jerome Valcke, who had been Sepp Blatter's right-hand man.
The two men have been under investigation since March in connection with media rights for the 2026 and 2030 World Cups on allegations including corruption, bribery, criminal mismanagement and forgery of a document.
Authorities in France, Greece, Italy and Spain have cooperated with the Swiss probe, including by raiding properties.
But the OAG only went public with the case on October 12,
Khelaifi's high-profile French lawyer, Francis Szpiner, then swiftly announced that his sports tycoon client "denies any corruption" and "wanted to be heard as soon as possible" by Swiss prosecutors.
But despite Khelaifi's eagerness to be questioned, his case may still move slowly as Switzerland has a track record of taking its time with major corruption probes. Bern opened an investigation targeting ex-Fifa boss Blatter in September 2015, but there are no indications that the case is ready for court.
The beIN Media group, which is headquartered in Doha, has insisted that its World Cup rights deals were "advantageous for Fifa", rejecting any suggestion that it got favourable treatment.
Valcke, a 53-year-old French national, has told the French sports newspaper L'Equipe that he "received nothing from Nasser."
An increasingly prominent figure in sports and media, Khelaifi oversaw PSG's 222 million-euro world record signing of Brazilian superstar Neymar in August.
The corruption accusations are the latest to rock world football which is still reeling from the events of 2015, when Fifa officials were arrested en masse at the governing body's annual conference.
Quatar has found itself routinely accused of corruption since controversially winning the right to host the 2022 World Cup, charges it has always denied.