The midfielder says he had a great time at Old Trafford but has revealed he missed out on the chance to bid farewell to his team-mates
The World Cup winner sealed his switch to the United States after falling out of favour at Old Trafford under Jose Mourinho, failing to make a single Premier League appearance this season.
Nevertheless, Schweinsteiger reflected on a "great time" at United, insisting that he did not want his departure to overshadow the club's game against Middlesbrough prior to the international break.
"They had a match away on Sunday so I couldn't really tell them because I didn't want to have the focus on me. I wanted to have the focus on the team and on the game - I was very happy that they won.
"I had a great time there, especially with my team-mates and the staff there. I enjoyed it."
Schweinsteiger says he opted to make the move to MLS as he sought a challenge that he believes he will get in Chicago.
"I like to challenge myself," the midfielder added. "This is a big chance to challenge myself. I know the results the last two years were not so good, but I can feel the vision.
"I can feel there is something going on and I want to help this club."