Zinedine Zidane has admitted that coaching France "could be a possibility one day" after the president of the French Football Federation identified him as his preferred successor for Didier Deschamps.

There has been persistent speculation about Zidane's future in charge of Real Madrid in recent weeks as they trail Atletico Madrid in the La Liga title race after being knocked out of the Spanish Supercopa and Copa del Rey.

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The 48-year-old coach has insisted he's focused on the Madrid job and has no plans to quit but has also refused to confirm that he intends to continue next season.

"My relationship with [FFF president Noel] Le Graet is good. We've known each other since 1998," Zidane said in a news conference on Saturday ahead of Real Madrid's La Liga match with Valencia.

"It could be an objective one day. I've said it before, when I started coaching 10 years ago, that it's something that could be a possibility one day."

"Right now I'm here," he said. "I'm enjoying what I'm doing here. In the future we'll see, you never know. But my mind is on the day-to-day here at Real Madrid."

Zidane was questioned about the France job after Le Graet named him as the leading candidate for the position in an interview with French radio station RTL on Saturday.

"If Didier leaves and I'm still here, the first person I'd see would be Zidane," Le Graet, who has been in charge of the FFF since 2011 and is running for a fourth term, said. "I have a really good relationship with him."

Deschamps -- a former teammate of Zidane at club and international level -- has managed France since 2012, winning the 2018 World Cup in Russia.

His contract was extended in 2019 to run until the 2022 World Cup in Qatar, the same year that Zidane's Madrid deal ends.

Zidane would not be drawn on whether a resolution to the Sergio Ramos contract saga -- with the Real Madrid captain's deal expiring in June, and talks over a renewal deadlocked -- was a condition for him staying in charge at the Bernabeu for 2021-22.

"I'm the coach of Real Madrid today and what I'll do is make the most of every moment I have," he said. "The rest, the future we don't ever talk about and we won't. It's the present, what we're doing now."

Madrid will have both Dani Carvajal and Lucas Vazquez back from injury for Sunday's match with Valencia, while Zidane also confirmed that the recovery of Eden Hazard -- who had been expected to be out for six weeks with a muscular problem -- is ahead of schedule.