Sky Italia says Milan have opened talks with Spurs over a fee for the Ivory Coast international. The Londoners are seeking around €20m to sell.
For their part, the Rossonero are prepared to sell players to help fund the move.
Andrea Conti and Davide Calabria could be moved on to make room for Aurier.
For his part, Aurier is keen to see the move happen, with talks well underway between his agents and Milan management.