However, he struggled to impress in the Premier League, with Ten Hag losing his job to Mourinho a year later.
Discussing Mourinho in an interview with FourFourTwo, Schweinsteiger said: "He apologized to me later. I gave him a handshake and said 'All good, don't worry'.
I would've liked to have played more, definitely, and with Paul Pogba and Zlatan Ibrahimovic, because those two players I think we could have achieved much more.
"But I'm grateful to the supporters for the way they welcomed me when I had the chance to play.
My dream was to play at Old Trafford again and it happened after a while, after training on my own, or with the under-19s or under-17s. Playing at Old Trafford again really meant a lot to me.
Asked about comparisons with his former Bayern Munich coach Pep Guardiola, he continued: "The biggest difference? Probably the whole way they look at football!
"I must say, I always had a pretty good relationship with Jose Mourinho. When we spoke, it was very respectful. I really liked his character. but his way of playing football and Pep Guardiola's way? They were different.
"I don't know," he added on claims Mourinho didn't select him because he had been trained to play the Guardiola way. "Maybe it was also a decision by the board.
"You need to understand: I injured my knee the season before, I said I was going to have treatment in Manchester, then the same injury happened again and the Euros were coming up, so I asked the club and Louis van Gaal if I could have the treatment in Germany. For a player, the most important thing is to be healthy and come back as soon as possible. That was my goal, so I decided it like that, but it was not a decision against Manchester United."