Bale has established himself as a player of great importance to Real Madrid since his world record move from Tottenham in the summer of 2013, but there has been speculation that he could leave the club.
Manchester United manager Louis van Gaal is reported to have sanctioned a £120 million bid for Bale, but Florentino Perez has since poured cold water over suggestions the player could leave the Santiago Bernabeu.
Ancelotti has followed the lead of his club president and himself moved to extinguish these enduring links to Manchester United, while there is also reported interest from Chelsea, stating that Bale will remain a Real Madrid player.
The Italian said: “Bale is an essential player for us. He's not leaving."
Real Madrid, meanwhile, will be back in La Liga action on Sunday - with Valencia their opponents - having not played domestically since the second week of December owing to their Club World Cup commitments and the winter break.
Los Blancos are on a 22-game winning streak in competitive action, but actually did succumb to defeat in their most recent outing - a 4-2 loss at the hands of AC Milan in a friendly held in Dubai.