The Premier League Player of the Month has garnered attention with 12 goals this season, prompting speculation that Real are tracking his progress, along with Liverpool and Tottenham.
Vardy, however, insists he has no intention of leaving the Foxes.
"It is all speculation, it is as simple as that," the 28-year-old said to Sky Sports when asked about Madrid's reported interest.
"I am happy with what I am doing at Leicester and long may that continue. It has been a brilliant start for myself as well as the team."
The 28-year-old added: "I have already doubled my tally from last year but I don't set myself any targets.
"I just want to keep on improving as much as possible and the way the season has started I could not ask for much more really."
Vardy has netted in nine straight League games - putting him one short of Ruud van Nistelrooy's record set in 2003.