Zidane promised to clarify Madrid's goalkeeping dilemma at the end of the season, with Navas and Thibaut Courtois vying for a starting berth.
Three-time Champions League winner Navas was demoted to second choice following the arrival of Courtois at the start of the campaign, though the Costa Rican started Wednesday's 2-1 LaLiga loss at Valencia.
Asked about his future post-match, Navas told reporters: "If the coach tells me to go, that's what I'm going to do. But I have a contract and my present is at Real Madrid."
"I will always try to give my best and convince the coach that I should play," he added. "I have a contract and I want to be here, but let's see what happens. Let's focus on finishing the season well.
"We have to, for the honour of the badge, go out and win the remaining [eight] matches."
Madrid suffered its first defeat since Zidane returned to replace Santiago Solari last month – Goncalo Guedes and former defender Ezequiel Garay consigning the capital club to its ninth league loss of the season.
Zidane's side – already out of the Champions League – is third and 13 points adrift of leader Barcelona.
"It's a difficult time," Navas said. "It's been a year that has not gone as we had hoped [prior to the season starting] but we must face up to it.
"We must face this moment and hopefully that will help us to learn from all the mistakes we have made this year so that we can enjoy what this club deserves in the next few years."