The former Real Madrid coach is on the brink of extending his contract with the Brazilian Football Federation.
But Bale can see Ancelotti in charge of United, saying on the Stick to Football podcast, "He did well at Everton. I think he would do great.
"He's not just a manager, he's a coach as well, and he can do the tactical stuff as well. When his son was the head coach in his second spell, he did a lot more tactically then, but I think we had a better team the first time.
"Wherever Carlo goes, he will do an amazing job, just because he gets everybody on board. If you go to a big club and got good players, whether they're performing at the time or not, like Man United, they have been in the last couple of weeks but prior to that haven't, they've got good players and he'll get the best out of good players.
"He'll simplify things. You see now with Michael Carrick, he's simplified a lot of things that the previous manager was doing and you're getting results. So that's Carlo's genius, getting the best out of players and making it simple."