The Chile international has been in sparkling form this season as the runaway Serie A leaders look set to cruise towards a 30th official Scudetto.
Vidal is Juve's top scorer in all competitions with 16 goals from 33 appearances, while his creative side is evidenced by six assists.
"I'm flattered by Real Madrid's interest," he told Marca.
"Everything is turning out great for me. I want things to continue like this for the rest of the season.
"We have to try and win the Europa League and Serie A. I want to win both titles."
Chile face a tough task to get out of Group B, in which they will face Australia, as well as 2010's finalists Spain and the Netherlands.
Despite the challenge ahead, Vidal hailed the confidence flowing through Chile's squad as they look to make an imprint on the world stage.
"I'm training to arrive at the World Cup in top form," he said.
"It's a young squad that dreams of doing big things in Brazil."
