Zinedine Zidane has been pressing Real president Florentino Perez for a defensive midfielder as an alternative to Casemiro.
Paul Pogba was on the club’s radar but is now set to join United in a world record £100million deal.
And according to Spanish newspaper Sport, Real have instead turned their attention to Matic who tops Zidane’s wishlist.
The club are hopeful an offer of £34million will tempt the Blues into a sale, however, the Serbia international has three years left to run on his contract.
And Antonio Conte claimed this week Matic is very much part of his plans for the upcoming season and is not for sale.
“Matic is a very important player for me, very important in my idea of football – he knows this,” Conte said.
“I’m delighted by his attitude and behaviour and I see commitment in him.
“I know that with work he can become a fantastic midfielder, one of the best in the world. He is not for sale.”