Bale was left out of Madrid's squad for last weekend's 3-2 win against Villarreal, amid growing speculation that he could be on his way out of the club at the end of the season.
But the 29-year-old's agent revealed in an interview earlier this week that his client wants to stay in the Spanish capital and is happy to see out the remaining three years of his contract, even if he is not part of his manager's plans.
Zidane refused to comment during a weekend news conference, although he did indicate that conversations have taken place with the player.
"No, I don't want to answer. I'm the coach of Real Madrid and [Barnett] does his job," he said.
"I have to think about the game, playing well, that's what worries me. I won't tell you anything about [the conversation]. Private conversations are private.
"It's what I have to do with all of the players, but it stays internal. With the players I talk about other things, not just their futures."
Bale is one of several first-team players facing an uncertain future at Madrid, with Zidane expected to be heavily backed to freshen up his stale squad ahead of next season.
The Frenchman, who returned for a second spell in charge two months ago, is also looking forward to a brighter future for the Spanish giants after a disappointing campaign this time around.
"Is it exciting? Yes, and for me more than anyone. I have to tell people as the coach that we will always think about doing things well," he said.
"We've won a lot and that will continue. The history of this club will always keep growing. As a coach I say that next year we will have hope to win many things, we will give our all in our work, win because of that work; you have to work a lot and well.
"We will do all we can because the fans are proud of their team."
Manchester United midfielder Paul Pogba has been repeatedly linked with a switch to Madrid in recent months, but Zidane once more refused to be drawn on the possibility of a big-money move.
"It's not just me that likes him, everyone likes good players," Zidane said. "He's a Manchester United player and I won't talk to you about opposition players."