Carvajal came through the youth system at the Bernabeu and has made more than 200 appearances for Madrid's first team in all competitions.
The 26-year-old is also Spain's first-choice right-back and has won four Champions League titles, one La Liga crown and one Copa del Rey during his time at the Bernabeu.
Carvajal has a contract with Madrid until the end of the 2021-22 campaign, but he has revealed that he wants to play in England before the end of his career.
"I do think about [leaving Spain]" Carvajal told Libero Magazine. "And I am clear that I want to play in the Premier League. It is an experience that I really want to have. I don't want to be left wondering what it would be like.
"But, on the other hand, I would like to spend my whole career here, which would be something very nice too.
"It is true that [with] Qatar, China... we should not trick ourselves, it is about money. I would really like to experience the Premier League, but we will see."
Carvajal, who is currently on the sidelines with a calf problem, last extended his contract with Madrid in September 2017.