The 21-year-old is a product of the famed academy system at Santiago Bernabeu.
He was a regular for their B team throughout his time in the Spanish capital, but took the decision to head for Germany last summer.
Carvajal has impressed during his short time in the Bundesliga and speculation has suggested that he could soon be heading home.
The youngster admits he would be open to the prospect of re-joining Real, with the club having inserted a buy-back clause in his contract.
Carvajal told Marca: "Yes, I would like to return one day (to Real). 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.
"It is something unthinkable to be nominated for the best right-back award in the league. At this level, to be considered one of the best in a major league like this makes me quite pleased. It means that I am doing things well."