The allegations against the powerful Qatari sports executive Al-Khelaifi and Valcke, who was Sepp Blatter's long-serving right-hand man at Fifa, relate to the sale of media rights for upcoming World Cups.
A statement from the Swiss attorney general's office (OAG) said the probe which opened in March centres on offences ranging from bribery, fraud, criminal mismanagement and forgery of a document.
The OAG indicated that Al-Khelaifi was under suspicion only for actions taken as the head of the sports media group beIN, which operates on five continents.
But the Qatar broadcaster issued a statement denying any wrongdoing, while confirming French authorities had raided the company's Paris offices following a Swiss request for cooperation.
“beIN Media Group refutes all accusations made by OAG. The company will fully cooperate with the authorities and is confident as to the future developments of this investigation,” it said in a statement.
Famed French football club PSG, which grabbed headlines in August for its record signing of Brazilian superstar Neymar, is not implicated in the investigation.
Valcke denied the allegations in an interview with French sports newspaper L'Equipe on Friday.
“They say there have been payments from Nasser to me in return for the sale of rights at a preferential rate. But I've received nothing from Nasser”, he told the paper.
“There has never been an exchange between Nasser and me. Never.”
Valcke left the OAG on Thursday evening after he was interviewed “as a suspect” by representatives of the Swiss attorney general and “disputes all the allegations”, his lawyer told AFP.
“Mr Valcke left the Swiss attorney general's offices where he was heard all day. He came out free, there is no coercive measure against him nor any bail payment,” his lawyer Stephane Ceccaldi said.
The OAG said there was a third suspect in the case but identified him only as “a businessman in the sports rights sector”.
Prosecutors said they had evidence indicating that Valcke “accepted undue advantages” from the businessman “in connection with the award of media rights for certain countries at the FIFA World Cups in 2018, 2022, 2026 and 2030”.
The Swiss OAG also alleged that Valcke had 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”.
The 2018 and 2022 World Cups will be played in Russia and Qatar respectively, while the 2026 and 2030 tournaments have not yet been awarded.
Questioned in Geneva
Valcke, a French national who also holds South African citizenship, was sacked from his post as Fifa's secretary general last year amid the corruption scandal that brought world football's governing body to its knees.
He became the subject of a separate Swiss corruption probe in March 2016 over criminal mismanagement during his Fifa tenure.
The previously disclosed allegations triggered his dismissal from Fifa and a ten-year ban from football.
Valcke was in Switzerland this week arguing an appeal at the Court of Arbitration for Sport in Lausanne, where he was trying to overturn the ban.
While Valcke was being questioned, authorities in France, Greece, Italy and Spain searched “properties” as part of the probe, Swiss prosecutors said, adding that no suspect in the case was currently in custody.
Unlike Valcke, whose career in world football is generally seen as finished, Al-Khelaifi's prominence in the sport has soared in recent months, especially following the Neymar signing.
PSG paid Barcelona a record 222 million euros ($264 million) for Neymar and Al-Khelaifi vowed that the acquisition would bring the Champions League title to the Paris side within two years.
PSG was bought by Qatar Sports Investments in 2011.
The new probe is the latest in a complex web of scandals that have rocked world football over the last two and a half years.
Dozens of corruption investigations are ongoing in Switzerland, the United States and elsewhere.
Many relate to the sale of broadcast and marketing rights, with Fifa insiders accused of taking kickbacks in exchange for sweetheart deals with broadcasters and promoters.
Fifa president Gianni Infantino, who took over from the disgraced Blatter last year, has vowed to clean up the game.