The Spain Under-21 international would be willing to make the move back to the Santiago Bernabeu after leaving the club during the summer
The 20-year-old left the Santiago Bernabeu side at the start of the season to try his luck in the Bundesliga and has since impressed with a number of fine performances.
Madrid included a buy-back option when selling the right-back, and a number of recent reports have suggested that the Blancos are ready to exercise their right, much to the delight of Carvajal.
"It isn't true that there's already an agreement, but obviously it would be a dream come true to return to Real Madrid," the defender told Marca.
Carvajal has made 18 official appearances for Leverkusen, scoring once in the process.