The England youth star, 23, has had a tough time with injuries during Antonio Conte's spell at Spurs and missed opportunities to impress.
Paolo Maldini, the Serie A champions' director, is looking to replicate the success of Fikayo Tomori, who signed from Chelsea last summer and thrived at the San Siro.
According to the Daily Mail, Milan are plotting a loan deal for Tanganga with an option to buy.
It is understood Spurs director Fabio Paratici has arrived in Milan for talks over the defender's future.
Tanganga burst onto the scene under Jose Mourinho in 2020, but a serious knee injury has tempered his trajectory.
Meanwhile, Paratici will reportedly discuss the future of Bryan Gil with Sampdoria while in Italy.
The Spanish winger, 21, underwhelmed after signing from Sevilla last season but spent an impressive second half of the campaign on loan at Valencia.
Tanganga and Gil have both returned to action for Tottenham on their pre-season tour of South Korea.
Spurs have been busy in the transfer window, striking deals for Richarlison, Yves Bissouma, Ivan Perisic, Fraser Forster, Clement Lenglet.