Germany midfielder Schweinsteiger is on United???s list of summer transfer targets along with Real Madrid defender Sergio Ramos.
The 30-year-old midfielder made just 15 starts for the Bundesliga champions last season and is believed to be interesting Old Trafford manager Louis van Gaal.
Beckenbauer helped Bayern to a hat-trick of European Cup victories between 1974 and 1976 before spending the final part of his playing career in America with New York Cosmos.
He feels that is a path Schweinsteiger should also follow rather than making a switch to the Premier League.
Beckenbauer said: “I would advise him not to go to England. He can stay here as well. This challenge, at his age, it???s not what he needs.
???I would play one or two more years in Munich, at this high level. And then, if he still wants to and if he still feels like playing football is the thing, he can make a step back and maybe go to the USA.
???In New York, Cosmos is searching for players, also Red Bull. So I think if he, as a world champion, goes to New York or another club in the Major League Soccer, that would greatly improve the standing of football there.”
Several newspapers have reported Angel di Maria could be used as a makeweight in any potential deal to take Schweinsteiger to Old Trafford.
Winger Franck Ribery has endured injury problems but Beckenbauer does not believe the Argentine international would be the right type of player to come in.
He added: “I think that nobody can replace Rib??ry and his way of playing football. Di Maria is more of an offensive midfielder in the centre.
???I do not think he’s a real winger. I don’t know the plans of Pep Guardiola or Matthias Sammer who are responsible for that. But I am convinced that Bayern will have a strong team next season.”