The Paraguayan striker, whose contract with Manchester City expired this summer, had been expected to sign for the Serie A side on Thursday.
But Bologna general director Roberto Zanzi has confirmed that no clear decision has yet been made by the player.
"The player has not decided yet," Zanzi told Corriere di Bologna.
"These are delicate choicesas there are different offers on the table.
"I've spoken with him many times in the last few hours. Let's wait and see whether he will decide to accept our offer or not."
Santa Cruz spent last season on loan at Malaga and they remain one of the clubs offering a contract to the former Bayern Munich star.
The 31-year-old has been quoted in Argentina as saying: "I'll choose where to play very soon. The choice will be between Turkish side Kasimpasa, Bologna, Malaga and the Brazilian side Palmeiras."