Ancelotti's words came at a press conference ahead of Los Blancos' European Super Cup clash with Sevilla in Cardiff on Tuesday evening.
"Gareth is now familiar with Madrid, the club, the city... I think he will exceed what he did last year. I see him in very good physical and mental shape. He will to rise. I do not know if he'll play tomorrow. Everyone talks about him playing at home, but he may start as a substitute," Ancelotti told reporters.
"Ballon d'Or? He's one of the best in the world, that's for sure. Last year was spectacular, his end to the season was very good. But beware, there is a lot of competition in this team. If I say that Gareth could win, I could also say that [Sergio] Ramos and Cristiano [Ronaldo] deserved it this year."
Bale, who arrived at Madrid from Tottenham Hotspur last summer, scored 22 times for the capital outfit last season.