The versatile 22-year-old has reportedly been a target for Madrid for some months and, according to Marca, has already told Zinedine Zidane's side that he would be willing to make the move.
"My future is the national team," he told reporters on Wednesday. "I'm 22, it's a dream for me to go to the World Cup. It's a unique opportunity.
"My future is training tomorrow and the game on Sunday, nothing more."
Odriozola's rise to prominence at Sociedad, as a defender and a winger, has been one of the club's real success stories of the last two seasons.
The 22-year-old, who only made his Spain debut against Albania in October, could even find himself starting their opening World Cup match against Portugal on June 15 if Dani Carvajal is unable to recover in time from a hamstring injury.
"Everything has changed a lot for me in a year and a half," he explained. "It's been mad but, as I call it, it's been a blessed madness.
"I have a privileged environment with my family and friends. The key is to work day to day, to know you have to improve. Trying to work and to sacrifice is what leads you to the beautiful things that are happening to me."