Louis van Gaal, who signed Schweinsteiger for Man United last summer, was sacked on Monday and Mourinho is widely expected to be named as his successor.
Schweinsteiger thanked van Gaal for the impact he had on his career but claimed that Mourinho can bring success back to Old Trafford.
“Also, my move to United was because of him. I will never say any bad words about somebody for whom I have so much to thank.
“Quite the opposite – even if we were not always of the same opinion, we had a good relationship. I admire him as a coach and despite a difficult season with really much injury misfortune, he still ended it with a good title. It’s been two years since United last won a title and I think that was a good ending also for him.
“We don’t know who will be our new manager yet, but it looks like it’s going to be an interesting derby in Manchester next season. The enthusiasm for football in Manchester is great and if Mourinho does take over at United, I think all of the players want to train under him so it’s going to be quite a special season.”
It will be interesting to see how Schweinsteiger fits in under Mourinho, if at all.
The German has enjoyed a highly successful career at the highest level with Bayern Munich and the national side but his debut season at United was a mixed one. After a promising start, Schweinsteiger eventually faded into the back of the mind, mainly due to injury.
But Mourinho is known to build his teams on a strong foundation in the middle of the park and Schweinsteiger may enjoy a new lease of life under the Portuguese.