Zidane was reappointed as Real boss this week and will be looking to guide the club to further success after previously winning the Champions League three seasons in a row.
As reported by The Mirror, Zidane is a huge admirer of De Gea, who has frequently been linked with a move to The Bernabeu in the past.
United recently triggered an option to keep De Gea at the club until the summer of 2020, and are in talks with the Spaniard over a new £350,000-a-week deal.
In 2015 Real agreed to sign De Gea but the deal didn’t go through due to the paperwork not being submitted in time.
Real paid £35million to sign Thibaut Courtois from Chelsea last summer.
However, it is believed that Zidane isn’t an admirer of Courtois; indeed he dropped the Belgian for his first game back as Real boss and started Keylor Navas instead.
Navas kept a clean sheet as Zidane’s side secured a 2-0 victory at home to Celta Vigo.
Zidane, enjoyed a winning return to the club he left nine months ago, as Los Blancos defeated Celta Vigo 2-0, and the Frenchman stated in his post-match press conference that he intends to make changes at the end of the season.
“There will be changes in the summer, but at the moment I cannot say more than that.
“I have a squad of 23-25 players, and I will not be here after each of our remaining games andd stating who will stay and who will leave. In the summer we will look at the situation and make decisions.”