Rumours in Spain surfaced on Tuesday that the 17-year-old was being targeted by the European champions, who believe Lee is becoming restless at the lack of gametime with the Camp Nou club.
Lee signed a civil contract with Barca - reportedly rejecting an offer from Chelsea that would've made him the highest-paid player in the UK at his age - as the Catalans are not allowed to sign new players on sporting deals in 2015.
However, this means the teenage talent cannot play in official matches for the Catalans' youth team, instead being restricted to friendlies and matches for South Korea's national youth teams.
Despite the restrictions on competitive fixtures Lee can play, his father has insisted that his son's time in Catalunya has been excellent, and claims any bid from the Blancos would be flattering but politely declined.
"We have not received any offer from Real Madrid," he told SBS. "We're thankful for interest from a big club but what Barcelona are doing for my son and the environment they made for my family is almost perfect.
"We don't have any intention of ditching them even if an offer actually came in. Interest from Spanish media are almost scary. But my son is doing well and he's focusing on his football."
The teenager's similar style of play to that of Leo Messi has seen him labelled the right-footed version of the Argentine star.
