The Italian head coach has been in charge in Turin since 2014 and the Old Lady have gone on to lift the Serie A title every year during his tenure.
Although Juventus' success in Europe has been underwhelming by their high standards, Allegri remains as one of the most in-demand managers across the continent and was even linked with the position at Arsenal prior to the appointment of Unai Emery.
A report from Tuttosport (via Calciomercato) claims that Real Madrid want to bring Allegri to the Spanish capital next season and that the reigning European champions have already made contact with the 50-year-old manager.
It is understood that Juventus are desperate to keep Allegri until the end of his current contract at least, which is set to expire in 2020.
But the report adds how Real Madrid's failure in approaching other targets have put Allegri at the top of their managerial wishlist this summer.
Liverpool boss Jürgen Klopp and Tottenham's Mauricio Pochettino remain in consideration at the Santiago Bernabéu. However, Madrid's original four-man shortlist was dashed to three after Hoffenheim manager Julian Nagelsmann turned his nose up at the opportunity.
German publication Bild (via Football Espana) explained how the 30-year-old manager would have been the cheapest option for Real Madrid to take.
But Nagelsmann, who has been widely dubbed the manager of the season in the Bundesliga, has rejected the chance of moving to Spain this summer.
Nagelsmann has a contract with Hoffenheim until 2021, but a release clause in his deal will become active next season - making a move away from the Rhein-Neckar-Arena easier to complete for any potential suitors.