Ramsey is set to leave Arsenal after the club opted against extending his contract, which expires at the end of the season.
Juventus head up a list of elite sides interested in getting the Welshman on board, with Real Madrid and Bayern Munich also sniffing around.
Ramsey has insisted he will stay with Arsenal until the campaign concludes but could already have a move agreed before then.
Boscolo says Juventus are pushing to snap up the 28-year-old before the end of the January transfer window.
And that’s motivated by their hopes of ending their European hoodoo with Massimiliano Allegri at the helm.
“I know that Juventus is trying to get him now because it could be important for the Champions League,” Boscolo told Tutto Mercato Web.
“He is an experienced player who will not have difficulty entering the Italian league and Allegri’s tactical chessboard.
“He brings quality and quantity, has important numbers.”
Aaron Ramsey would have to compete with the likes of Miralem Pjanic, Blaise Matuidi, Rodrigo Bentancur, Emre Can and Sami Khedira for a starting spot at Juventus.
Boscolo believes Ramsey has plenty to offer Allegri if he trades the Emirates for the Allianz Stadium.
“The ideal position? He is a midfielder that does the two phases well, like [Claudio] Marchisio,” Boscolo added.
“He can assist and score, he can give something more to the Juventus midfield.”
Ramsey came on as a substitute during Arsenal’s 1-0 defeat to West Ham last weekend.
That result left Unai Emery’s fifth in the table, six points adrift of fourth-place Chelsea.
Next up for the Gunners is Saturday’s showdown with Maurizio Sarri’s Blues.