Odriozola is expected to leave Real Madrid before the end of the transfer window on Tuesday with Fiorentina pushing to sign him.
The Italian club have an agreement in place with Real Madrid to sign him on loan and have already spoken with the player as well.
The Spaniard is assessing his options and is yet to give his consent to a move to Fiorentina this summer.
And according to Italian outlet Tutto Mercato, Tottenham have arrived in the picture and they want to take him to north London in the next few days.
Tottenham are looking to sell Aurier before the end of the transfer window on Tuesday but they also want a replacement for the Frenchman.
And the Real Madrid full-back has been identified as the player who could replace Aurier in the squad.
Tottenham have already held talks with Real Madrid, but for the moment Fiorentina have the edge in the race as they have a deal in place with the Spanish giants.