The Rossoneri are contemplating whether to make a formal approach for the 22-year-old defender, who has a contract at Spurs until 2025.
The Englishman has enjoyed a productive season in the Lilywhites backline, making five appearances since Boxing Day.
However, Sky Sports News claims that the centre-back has concerns regarding his long-term future at the Tottenham Hotspur Stadium.
The report adds that Tanganga feels that he may drop down the pecking order once Eric Dier and Cristian Romero have returned from injury.
The Italian giants are said to be monitoring the situation in the event that the centre-back is made available on loan.