After making 18 Premier League appearances last season, 32-year-old Schweinsteiger has failed to turn out for United since the Portuguese coach replaced Louis van Gaal in the close season.
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Schweinsteiger has also been left out of the side's Europa League squad, with Mourinho confirming that it would be "very difficult" for him to play for the club again.
"I believe that Manchester United could 100 percent benefit from a fit Bastian Schweinsteiger," Gundogan told Sport Bild magazine. "He's not just some player, and also not only 18 or 19."
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Gundogan, who was named in Germany's squad for this month's World Cup qualifiers after almost a year out of the side due to injury problems, believes he can fill the void for his country following Schweinsteiger's international retirement.
"I trusted myself to do that before [Schweinsteiger's retirement], but this has nothing to do with saying his retirement is positive or negative. We should be thankful that we had such a great player," he added.
Germany face the Czech Republic on Saturday and then host Northern Ireland three days later in the World Cup qualifiers.
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