Schweinsteiger joined Man United from Bayern Munich in the summer of 2015 and made 31 appearances during his first season in English football.
The 32-year-old has been frozen out under Jose Mourinho this term, however, and Gundogan has blasted the Red Devils for their treatment of the World Cup winner.
"I believe that Manchester United could 100% benefit from a fit Bastian Schweinsteiger," Gundogan told Sport Bild. "If everything you hear and read is true, you can consider it disrespectful. He's not just some player, and also not only 18 or 19."
A number of clubs have been linked with a move for the experienced midfielder, including MLS side Dallas, who revealed their interest towards the end of last month.