Zidane's return puts Bale's future in further doubt, given the pair's relationship became strained last season, before the Welshman said he was considering his future at the club.
Zidane replaced Santiago Solari on Tuesday on a contract until 2022 with Madrid out of the Champions League and Copa del Rey, and lying third in LaLiga, 12 points adrift of leaders Barcelona with 11 matches left.
Mbappe's team-mate Neymar is also thought to be of interest to Madrid, and while Zidane would not be drawn on transfer plans, he did reference the two PSG players' elite ability.
"I think Jose Mourinho would have been a step backwards, there was a lot of problems and controversy when he was here".
"I am not thinking about that, we have to think about finishing the season well", Zidane said.
"I think it is ideal and fantastic", the former Chelsea boss said, even as he was quick to add he was never disappointed by Madrid's decision not to hire him.
"We know what they are like, but having said that the only thing in my head is the game tomorrow and nothing else".
Real president Florentino Perez has again turned to Zidane, who stepped in for Rafa Benitez in 2016.
"Now he has a new project, he can start afresh and prove to everyone how talented he is, so I wish him all the best".
"And of course that VAR, even though for me it's a penalty, you can still be unlucky and not get it in the last minute and then we'd be out and no one would really remember the PSG performance".
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