Zidane has regularly been linked with managing his native France, with incumbent head coach Didier Deschamps recently tipping him to succeed him in the role.
French Football Federation president Noel Le Graet, meanwhile, has said Zidane would be the first person he would call should he ever need to replace Deschamps.
Ahead of Madrid's home match with Valencia on Sunday, Zidane was open about his aspirations.
"I am passionate about football and you never know about the future," he said.
"My relationship with Mr Le Graet is long, since 1998.
"The national team is a goal, like I said when I started coaching 10 years ago, but now I'm here.
"We will see. My mind is here. I am at Madrid and I enjoy every day."
Zidane added: "We know the pressure that comes with representing Real Madrid. We do our own thing, what we can control.
"We know we can achieve great things and we are going to put all our energy into these two [remaining] competitions."
Madrid are eyeing a fourth win in five matches when they host mid-table Valencia.
But after winning the reverse fixture 4-1, Valencia are looking to complete a league double over Madrid for the first time since 1967-68 season.
To do that, they will need to end a long streak.
Madrid have avoided defeat in their past 12 home LaLiga games against Valencia (seven wins and five draws) since a 3-2 loss in March 2008, and they have scored at least two goals in nine of them.