The Bayern Munich president knows the German midfielder well from his 17-year stay at the Bundesliga champions.
Schweinsteiger only left Bayern last year in a £6.5million move, signing a three-year deal as Louis van Gaal attempted to strengthen his United squad.
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He did struggle to stay consistently fit in his first season at Old Trafford and could do nothing to stop van Gaal leaving the club after a disappointing campaign in charge.
But Schweinsteiger is a Champions League and World Cup winner and, despite being 32, is still a quality player when healthy.
Jose Mourinho obviously disagrees, exiling Schweini from the first team, forcing him to train with the youth team, according to reports.
He’s been linked with a return to Bayern – something new Munich manager Carlo Ancelotti has denied.
And despite ignoring talk of going after Schweinsteiger, Rummenigge has criticised United for their treatment of the German legend.
Speaking in an interview with sueddeutsche.de, Rummenigge said: “I could hardly believe when I read it. This never happened before at Bayern Munich and never will happen.”
“In the future players will think twice before joining such clubs, who treat them more radically when they want to get rid of a player than a club like Borussia Dortmund or Bayern Munich in the Bundesliga would do.
“It seems like this is the price players have to pay if they join these clubs.”
That’s a pretty robust attack from Rummenigge on Mourinho and United when neither Schweinsteiger or the club have confirmed that he’s been frozen out.