Both Karl-Heinz Rummenigge, Bayern’s chief executive, and Philip Lahm, the club captain, have now entertained the possibility of Schweinsteiger returning to Bavaria, a year after leaving for Manchester.
"Should he [Schweinsteiger] speak in the future at some point about a desire to return, then we will discuss it with him," Rummenigge told Bild.
"It is important to involve players," Lahm said. "A man like he was predestined to work in the team, he knows everything and everyone."
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Schweinsteiger’s brother Tobias, who works as Bayern Munich’s Under-17s team, appeared to criticise Mourinho’s treatment of Bastian on Monday.
Following reports of Bastian’s demotion to the reserves, the retired, elder Schweinsteiger tweeted: “no respect”.
Schweinsteiger was signed by Louis van Gaal, Mourinho’s predecessor at Old Trafford, last summer, but struggled for both fitness and form during his debut campaign.
The Germany international and World Cup winner made only four appearances after suffering a knee injury in early January.
His absence from the club during his rehabilitation period led some of his teammates to believe that he was afforded "special treatment" by Van Gaal.
Schweinsteiger spent a total of 17 years at Bayern, graduating through the club's youth ranks and making his first senior appearance in 2002.
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