Manchester United pair Victor Lindelof and Raphael Varane were raised inside Real Madrid.
Real are short of defensive options with Eder Militao and David Alaba both recovering from ACL injuries.
The Athletic says Real chiefs suggested Lindelf, Varane and Raul Albiol, of Villarreal, as potential stop-gap signings.
However, Real Madrid's management were left unconvinced by all three options.
Real coach Carlo Ancelotti has since stated this week: "We will not sign another centre-back.
"We have players like (Aurelien) Tchouameni who can cover that position.