Varane was the third choice centre-back at the Bernabeu behind Pepe and Sergio Ramos for much of last season.
The defender has suffered for not playing regularly at club level and was also left out of Real’s Champions League semi-final double-header with Manchester City – before missing the final through injury.
He was also left out of their Champions League semi-finals with Manchester City.
And Spanish newspaper Marca claim Varane is getting tired over being overlooked.
According to the report, Manchester United have shown the most interest in the 23-year-old and could come in with a bid this summer.
However, Real are not looking to sell and so Varane must instigate any move himself by telling Bernabeu bosses he wants to quit.
Zidane has made it clear he wants Varane to stay but reportedly won’t stand in his compatriot’s way should Varane ask to leave.
New United manager Jose Mourinho is credited with bringing Varane into the Real first team when he was boss at Madrid.
Varane made his debut at Real under Mourinho in 2011 after signing from Ligue 1 side Lens.
United have already signed a centre-back this summer in Eric Bailly, who cost £30million when completing his move from Villarreal.
Bailly is United second defensive arrival from the past four transfer windows, with Matteo Darmian of Torino signing for the club last summer.
As for Varane, Marca claim he is also worried about his international future if he is not a regular at club level.
He was ruled out of Euro 2016 with injury, leaving Sevilla’s Adil Rami to partner Laurent Koscielny in the heart of defence.