That is according to Liverpool legend and pundit Steve Nicol, who believes the 28-year-old has not got long left to achieve the success that he wants.
Sanchez is out of contract at Arsenal at the end of next season and has been heavily linked with an exit from the Emirates.
Both Bayern Munich and Manchester City are interested in signing the Chile international, with a move of around £40million to the German champions touted in the last few days.
Nicol believes that to match his ambitions, Sanchez should choose Bayern because they are most likely to succeed both domestically and in Europe.
Steve Nicol says Alexis Sanchez should leave Arsenal for Bayern Munich, not Man City Paper gossip: Bayern Munich step up Sanchez chase, Man Utd eye £60m Morata bid Fri, June 9, 2017
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So with Alexis Sanchez having quite a small window for achieving the success that he wants, I would chose Bayern Munich
Steve Nicol on Arsenal star Alexis Sanchez
“I think I would go for Bayern,” he said on ESPN FC.
“I think he’s at the stage of his career where over the next two or three years, it has to be success. Then he’s going to start going over the hill.
“I think Bayern are just a little bit ahead of where City are.
Steve Nicol says Arsenal star Alexis Sanchez is likely to win more trophies with Bayern Munich
“You probably know you’re going to win the Bundesliga, you certainly know you’re going to get through the qualifying stages of the Champions League.
“So with him having quite a small window for achieving the success that he wants, I would chose Bayern.”