Bale was heavily linked with a move to Jiangsu Suning during the close season but the deal fell through and he remained at the Santiago Bernabeu.
Reports this week suggested Madrid will offer Manchester City £70million (€81m) and the 30-year-old in exchange for Raheem Sterling.
However, Zidane has no doubt Bale has an important role to play for Madrid beyond the January transfer window.
"I want Gareth to stay here until the end of the season," Zidane told a news conference ahead of Wednesday's Champions League home game against Galatasaray.
"People keep saying that I want him to leave in January, it's nonsense. Our fans have to think positively, as the player wants to be with us.
"He has returned here and wants to recover, but he simply hasn't recovered yet."
👔🗣️ #Zidane: "It's both responsibility and excitement to play a match like this at home. What we want to do is play a good game, and for that we have to be prepared."#RMUCL | #HalaMadrid pic.twitter.com/HWVv5Vb5LO— Real Madrid C.F. 🇬🇧🇺🇸 (@realmadriden) November 5, 2019
Bale has not featured for Madrid for a month, having sustained an injury during Wales' 1-1 draw with Croatia on October 13.
Despite that fact, Bale has been named in the Wales squad for crunch Euro 2020 qualifiers against Azerbaijan and Hungary, with Ryan Giggs stating the winger had assured him he would arrive ready to play.
"He's not training normally, so we'll see on a day-to-day basis. His country has a right to pick him, it's a FIFA date so we can't do anything about that. But what the player wants is to be fit and ready," said Zidane.
"He's been back training in the last week and we'll see if he's ready to play for his national team, but the shame for us at the moment is he's not ready to play for us."
Zidane denied he has strained relationship with Bale, adding: "We say, 'Good morning' to each other every day.
"I love all my players. We can't all have the same close relationship but I've never had any problem with Gareth, even when there was talk of him leaving. I'm happy with him.
"You [the media] need to stop always saying the same thing or asking me about him leaving matches early, because I used to do the same.
"The important thing is that he was with the team before the match and at half-time to support them.
"You look for things that aren't there. He wants to see the team win, I have no doubts about that."