Having missed much of last season due to a double knee injury, Carvajal's current deal has just over a year to run.
He told FIFA's website: "Yes, it is clear that the day I am no longer at Real Madrid, or the day we decide together not to continue, I would like to try another league that is not in Europe, and the MLS is one of the candidates."
Carvajal expects to be part of Real Madrid's Club World Cup campaign and also said: "After all, it is a new tournament, a World Super Cup, as the name suggests. The best teams in the world are competing against each other and both the club and I personally are very excited about it.
"Mixing different types of football, different leagues, different continents makes it very special. This year we have already faced both Pachuca and Salzburg. We have experience and we can't wait to get started."