The Qatari, who masterminded the record-breaking £199million signing of Neymar this summer, is also chief executive of TV company BeIN Sports.
Swiss prosecutors suspect former FIFA secretary general Jerome Valcke “accepted undue advantages” from Al-Khelaifi “in connection with the award of media rights for certain countries at the FIFA World Cups in 2026 and 2030”.
In a statement, the Swiss attorney general said the new proceedings involved suspected cases of bribery, fraud and forgery against Valcke and Al Khelaifi, who is the chief executive of the beIN Media Group.
The statement read: “It is suspected that Jerome Valcke accepted undue advantages from a businessman in the sports rights sector in connection with the award of media rights for certain countries at the FIFA World Cups in 2018, 2022, 2026 and 2030, and from Nasser Al-Khelaifi in connection with the award of media rights for certain countries at the FIFA World Cups in 2026 and 2030.
“As it announced in March 2016, the OAG (Swiss Attorney General) is already conducting a proceeding against Jerome Valcke, in particular on suspicion of various acts of criminal mismanagement. This proceeding is still ongoing.
“The new proceeding has been opened primarily on the basis of findings obtained by the OAG in the earlier proceeding.”
The beIN Media Group said it “refutes all accusations made by the OAG” and will co-operate fully throughout the investigation.
In a separate statement, the French Justice Ministry confirmed two judges from the National Financial Prosecutor’s Office had conducted a search of the Paris offices of beIN Sports, at the request of the Swiss public prosecutor.
Al-Khelaifi, 43, was appointed chairman and chief executive of PSG in 2011 shortly after the club’s buyout by a Qatari-led consortium.
Valcke was sacked by FIFA in 2016 after being implicated in an alleged scandal involving ticket sales and misuse of expenses, the result of a probe by the US Department of Justice which also brought down his boss, the then-FIFA president Sepp Blatter.
Valcke is already banned from FIFA for 10 years. He launched his case at the Court of Arbitration for Sport in Lausanne this week to challenge the ruling.