The Juventus midfielder has been identified by the Italian tactician as a man he wants to bring to Spain, if - as expected - he replaces Jose Mourinho at the Santiago Bernabeu ahead of the new season.
Manchester United have held a long-term interest in 26-year-old Vidal, who has established himself as one of the best box-to-box midfielders in world football since moving to Turin in 2011.
However, the Premier League champions will face serious competition to sign the Chile international, now that Real Madrid have emerged as contenders for his signature.
Juventus would prefer to keep hold of Vidal - who still has three years to run on his contract - however, Antonio Conte might be prepared to sell if a club meets the player's £30million valuation.
Given the fact that the reigning Serie 'A' champions are also interested in signing Gonzalo Higuain from Real Madrid, Spanish newspaper El Confidencial suggests that Ancelotti could offer the Argentinian as bait to tie up a deal for Vidal.
That would put pay to Manchester United and Manchester City's hopes of luring the Juventus star to Old Trafford or the Etihad Stadium, if the current Paris Saint-Germain boss is appointed as Real Madrid's new manager later this summer.