The Times reported that police believe Milone, the former chairman of Deloitte Italy, had individuals followed and photographed.
Milone spoke to reporters last month, breaking silence since his sudden resignation as auditor general half way through his contract, in June.
He said he feared prosecution over “fabricated’ evidence surrounding his use of an external IT firm, which lead to his resignation.
However, he defended his use of the firm and said he hired them in reaction to tampering on his and his staff’s devices.
Holy See secretary of state archbishop Giovanni Angelo Becciu said Milone had overstepped the line and was “spying on the private lives of his superiors and staff.”
“If [Milone] had not agreed to resign, we would have prosecuted him,” Becciu said.
Milone was originally hired by Pope Francis in 2015 as an independent auditor tasked with cleaning up questionable finances.
His appointment came a month before over €1bn hidden off the Vatican’s books were identified by Cardinal George Pell.