Italian police, who searched the villa yesterday, said Khelaifi had used the property as "a means of corruption".
Khelaifi and Valcke, who was Sepp Blatter's right-hand man at FIFA, were placed unber investigation by Swiss prosecutors yesterday over the sale of World Cup media rights.
FIFA said yesterday it was also investigating Khelaifi, a Qatari, over the media rights issue.
The world football body's Ethics Commission "opened a preliminary investigation into Nasser al-Khelaifi on Thursday evening", a FIFA spokesman said.
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Several people "linked to various titles to the company that owns the villa" have been questioned, police added.
Valcke's lawyer denied any wrongdoing, telling AFP his client had paid rent for the villa.
"There was a contract and Mr Valcke paid the rent," Stephane Ceccaldi said.
The Swiss attorney general's office said their probe into Valcke and Khelaifi focused on media rights for upcoming World Cups between 2018-30 and includes allegations of bribery, fraud, criminal mismanagement and forgery of a document.
The Qatar broadcaster has denied any wrongdoing while confirming French authorities had raided the company's Paris offices at the request of Swiss authorities.
Khelaifi oversaw Paris Saint-Germain's world record signing of Brazilian superstar Neymar in August.
The audacious 222 million euro transfer from Barcelona was widely seen as an example of gas-rich Qatar, which will host the 2022 World Cup, exercising its "soft power".
The club, which was bought by Qatar Sports Investments in 2011, is not implicated in the Swiss investigation.