The 22-year-old has been a revelation in the Basque country over the last couple of years, with the right-back playing 35 of his side's 38 La Liga games this season an earning a place in his country's World Cup squad.
With the World Cup on the horizon, it now appears that the youngster could be on the verge of a move to Real Madrid, with the club needing only to agree a fee with Sociedad to make the deal happen.
At the moment, the Basque side are holding out for the full €40m that Odriozola's release clause is set at, though Madrid are believed to be hopeful of bringing that figure down buy including some of their fringe players, who Sociedad are known to be keeping an eye on, in the deal.
Zidane has been a long-term admirer of Odriozola and has reportedly moved a deal up his list of priorities after a series of uninspiring performances from youngster Achraf Hakimi over the course of this season.
Though any deal will have to reach the €40m figure of his release clause, Madrid are thought to see that as a reasonable fee given the recent explosion in transfer prices and the fact that the Basque is attracting plenty of interest from other European heavyweights.