Rodriguez was left out of Real Madrid's squad for yesterday's Champions League final against Juventus.
Spain's two major newspapers AS and Marca claim the Colombia international will leave in the summer as a consquence of his declining influence at the Bernabeu.
After starring at the 2014 World Cup, Perez made a determined effort to sign Rodriguez but the midfielder has struggled to live up to his high price tag.
And this season the 25-year-old hasn't been able to break into Zidane's starting XI regularly.
How Man United could look with James Rodriguez Tue, May 16, 2017
Is this how Manchester United could look if they sign James Rodriguez from Real Madrid?
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Is this how Manchester United could look if they sign James Rodriguez?
We'll speak with the coach; he is the person who will decide the future
Real Madrid president Florentino Perez
Manchester United have been linked with a move for Rodriguez.
But Perez says a final decision on the player will be made by Zidane.
"We're going to speak with Zidane, who's the conductor of this orchestra," he told Antena 3.
Zinedine Zidane will determine James Rodriguez's Real Madrid future
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"If it were up to me, everyone would stay.
"James is an incredible player, but when you have so many.
"I'd have everyone stay. We'll speak with the coach; he is the person who will decide the future."