Spurs have agreed a £23m fee for the defender as well as completing personal terms, but the deal has been delayed due to Aurier's criminal conviction in France last year.
The 24-year-old was found guilty of assaulting a police officer outside a Paris nightclub and given a suspended two-month prison sentence.
Aurier has protested his innocence and denied the charge, but Spurs must still seek clearance from the Home Office for him to enter the United Kingdom and complete his move.
The Ivory Coast international was forced to miss a Champions League game against Arsenal last term after he was denied permission to enter the country due to his conviction.
Spurs have only made two new signings so far this summer, although they are hopeful of completing the Aurier deal in addition to bringing in Juan Foyth from Estudiantes before Thursday's transfer deadline.