Paletta, who has made three appearances for Italy, joined Milan for the bargain price of €2.5 million (US$2.84m) last season just as Parma were on the brink of financial ruin that has since sent them plummeting to Serie D.
A report in the Gazzetta di Parma said Galliani's name had been evoked during court sessions in Parma relating to the purchase of Paletta, amid an ongoing investigation into the collapse of the club last season.
Milan released an official statement which said the player's transfer was fully above board.
"In relation to the news that Adriano Galliani has been mentioned in the investigation by the Parma Tribunal regarding the purchase of the football player Paletta, A.C. Milan would like to underline the legality of the operation and the club are sure that the magistrates will come to the same conclusion," said a club statement.
Paletta has since moved to fellow Serie A side Atalanta on a one-season loan deal.