Since replacing Santiago Solari during the second half of last season, Zidane has failed to rekindle the magic that saw him bring three consecutive UEFA Champions League titles to Madrid between 2016 and 2018.
Thursday's (AEST) humbling 3-0 defeat to Paris Saint-Germain in Europe's top competition led to fresh questions about his future, although former Madrid boss Mourinho declined to put himself forward as an alternative during an interview with Deportes Cuatro on Saturday (AEST).
"There are two types of rumours. One, when one speaks about Zidane, who is one of ours and it hurts us when our teams aren't going well," he said.
"You have to live with it. Zidane is in football all his life and he knows it. The other type of rumour is to put my name in there and I don't like that. There are problems in many places, but another thing is [to have] respect.
"I wouldn't like to return [to Madrid] because they have a manager and I can't coach a team who have a manager.
"You can speak with respect about the club but also about the manager, who isn't just anyone.
"I am out of it. I'm not just blowing smoke. I would like that things turn out well and everything gets fixed."
Mourinho suggested the picture in the Spanish capital is not as gloomy as some make out, pointing to the early standings in LaLiga, where Madrid is ahead of champion Barcelona by a point and can overtake leader Sevilla with victory at the Ramon Sanchez Pizjuan this weekend.
"They're third or fourth, no? Close to being first. It's not bad," he said.
"If you look at if pragmatically, if you focus on the table, they're right there.
"Now, they play Sevilla and if they win, they go ahead of them. Barcelona are behind them and Atletico are a point ahead."
Mourinho suggested he could be ready to take his talents elsewhere when he goes back to work, with a piece of information that is unlikely to go unnoticed in the Bundesliga's upper echelons.
"Now, I am in German classes in case one day I end up there, or so I can speak one day in this language for a [UEFA] Champions League game," he added.
"It will be my sixth language."