The Frenchman is widely expected to step down as Madrid coach during the close season, and confirmation of that could come as soon as Sunday (AEST).
Villarreal, which faces Manchester United in the UEFA Europa League final next Thursday (AEST), provides the opposition for Madrid's final match of the campaign.
There is a chance Madrid could finish as LaLiga champion, but it heads into the fixture with a two-point deficit to Atletico Madrid, which travels to Real Valladolid.
That would be an ideal way for Zidane to bow out of his second spell in charge of Los Blancos, although the most likely outcome is that his team finishes runner-up.
When it was mentioned to Zidane in his pre-match press conference that the players would welcome him staying on, the 48-year-old said: "I love my players very much. They have saved me on the pitch, in the sense that they have always given everything in every game.
"That they think that for me is very nice as a coach."
Three-time FIFA world player of the year Zidane has won three UEFA Champions League titles with Madrid and LaLiga twice.
Asked whether Madrid could be a better side without him, Zidane gave a surprising response, saying: "Sure, sure."
He repeatedly refused to answer whether his mind was made up on his future.
"We are going to play tomorrow, that's the important thing. We have time to talk about that. This is not the time," Zidane said.
"We must put all the energy into tomorrow's game After 37 matchdays we are not going to waste time talking about next year. We are only focusing on tomorrow's game.
"The important thing is not what I am going to do, but the team. I repeat myself, I'm sorry."
A barren season on the trophy front would be a sorry way for Zidane, the galactico turned superstar boss, to make his exit.
He could yet become the first Real Madrid manager to win two league titles in a row since Leo Beenhakker's three between 1987 and 1989, and Zidane may hope Villarreal's focus is on its European final.
However, Villarreal, which is seventh heading into the weekend, will want to guarantee a place in next season's European competitions through its league placing, so it is not a dead game for it either.
Madrid has only won two of the past seven meetings with Villarreal in LaLiga (D4 L1). However, promisingly for Zidane, both of those wins came in its past two home league games (3-2 in May 2019 and 2-1 in July 2020).
If Madrid misses out on the title, Zidane accepts there will be disappointment, but he said: "My players cannot be blamed for anything. Injuries, COVID, there have been many things.
"You can always do better and I am always critical of myself. I am a winner and I don't like to lose. In my life I fight and I give everything to win. And the players also want to win."