The 21-year-old has impressed at the BayArena since his move from Los Blancos in the summer and has even been nominated for the Bundesliga's best right-back award.
Reports suggest that the Spanish giants may look to bring him back to the Bernabeu in the summer, and Carvajal revealed that his former club have a buy-back option.
"Yes, I would like to return one day [to Real]," he told Marca. "They have an option to buy me back, too.
"I am trying to work the best I can here, to improve day-by-day and if one day they decide to exercise the option to bring me back, then I would accept it straight away."
Carvajal has won two caps for Spain's Under-21 side.