Veteran defender Marcelo and Wales forward Gareth Bale are the most high profile names whose futures look uncertain under Zidane, while Dani Ceballos, Marco Asensio and Toni Kroos all have points to prove to their returning coach.
"I would love to coach Mbappe, as all the good players".
Having left the club last summer, Zidane returned to Real on Monday after the side were eliminated from both the Copa del Rey and Champions League in humiliating fashion. "But this is not the moment to talk about that".
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"Gareth wanted to play one way and Zidane wanted him to play another", Barnett told the BBC's Football Daily podcast.
Gareth Bale has failed to take the mantle from Cristiano Ronaldo in terms of leading Los Blancos' attack, and despite rumours linking him with a summer move away from the Spanish capital, Zidane has refused to criticise the Welshman.
"They should not think I am looking at who will go, who will stay", he said. "I am not here to make any lists, I am here to finish the season well, all together". I'm not going to talk about players who are not mine. "The important thing is to all be ready, and I will count on everyone, including Isco [who barely featured under Solari] and all the others".