Valcke denied the allegations in an interview with French sports newspaper L'Equipe on Thursday.
Valcke also allegedly accepted "undue advantages" from an unnamed businessman in the sports rights sector in exchange for the same favorable intervention for the FIFA World Cups in 2018, 2022, 2026 and 2030.
Former FIFA general secretary Jerome Valcke has denied receiving "undue advantages" from Nasser Al-Khelaifi, the chief executive of Qatar's beIN Media and president of Paris St Germain, after Swiss prosecutors opened a criminal investigation.
Italy's financial police said in a statement the villa in Porto Cervo is owned by an international real estate company, and eight people were questioned.
Last year, The Office of the Attorney General of Switzerland (OAG) said it was investigating Valcke for "various acts of criminal mismanagement".
"I refute the accusations against me or Nasser".
BeIN said the group "refutes all accusations" and that "the company will fully cooperate with the authorities and is confident as to the future developments of this investigation".
"There was a contract and Mr Valcke paid the rent", Stephane Ceccaldi said.
Valcke was Sepp Blatter's right-hand man when the latter ran FIFA, the Swiss-based world soccer body.
The new proceeding has been opened primarily on the basis of findings obtained by the OAG in this earlier proceeding.
beIN Sports, formerly Al-Jazeera Sports, is one of the most powerful broadcasters in world football, owning broadcast rights across the Middle East and North Africa including for Champions League and European Championship matches.
The OAG said the investigation relates to "bribery of private individuals, fraud, criminal mismanagement and forgery of a document".
Valcke is serving a 10-year ban from football after he was found guilty by FIFA's former ethics judge Hans-Joachim Eckert of misconduct over the sale of World Cup tickets, abuse of travel expenses, attempting to sell TV rights below their market value and destruction of evidence.
As a result, he was sacked by FIFA and banned from football for a period of 12 years in January 2016, which was reduced to 10 years in June.
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