The Englishman, who struggled with knee problems last season, wants to try a new challenge where he can play regular football.
According to transfer expert Gianluca Di Marzio, the 23-year-old's agent has been in touch with Milan.
Di Marzio said: "During the day there was also a meeting with Tanganga's agent, a young Tottenham defender who hasn't played much in the last period of the season.
"He needs to recover, he wants to try a new experience. He is a name on the list, there is still no negotiation between Milan and Tottenham."