But he insists that the German giants will not pay “crazy sums” to secure the Arsenal forward.
Sanchez’s future with the Gunners remains up in the air with contract negotiations seeming far from a conclusion.
Bayern were linked with a move for Sanchez early in the transfer window, but Manchester City are now the heavy favourites to land the Chilean.
However, speaking to the media this weekend, Ancelotti has admitted that Bayern are ready to make their move – if he comes at a reasonable price.
Ancelotti said: “If an opportunity comes up, the club will be ready.
“There are lots of rumours. Alexis is a great player but not the only one in the world. I like Alexis.
“There are possibilities in the transfer market, which can be in many directions.
“I believe that the market is currently somewhat crazy – and Bayern is not a crazy club.
“I know the culture of this club and will not ask for any players for whom the club has to spend crazy sums, but if there are occasions, why not?”
Sanchez will be playing for Chile in the Confederations Cup final on Sunday evening, as he is set to embark on a year-long season.
He will link up with Arsenal for pre-season almost immediately after the competition comes to an end.
By the end of the Premier League season, Sanchez will be hoping his attention will be on representing Chile at the World Cup in Russia next summer.