The former Germany captain, 32, was frozen out by Mourinho and forced to train away from the first team earlier this season.
But he was welcomed back into the senior squad at the end of October - and made his first appearance in 255 days as a late substitute when United beat West Ham 4-1 in the EFL Cup on Wednesday.
He came on to a huge round of applause from the home fans, whom he thanked afterwards for their support during his Old Trafford exile.
Schweinsteiger's United career looked to be over when he was sidelined by Mourinho, and a January transfer window move away looked on the cards –- even though the midfielder insisted he would see out a contract that expires after the end of the 2017/18 season.
But Mourinho now sees the World Cup winner staying on, with the United manager saying Friday: "When you have a contract with a club, you are the powerful one. You are the one who can decide your future.
"In the summer, we tried to make something happen for Bastian to get a different future. He was the powerful one," explained former Chelsea boss Mourinho, who once referred to himself as 'The Special One'.
"He decided to stay even in difficult circumstances.
"He worked for that and he deserved that little happiness he got from the last match.
"In January he will be the powerful one, and probably with better feelings than before now he is working with the team. He understands our dynamic and philosophy. You can see the happiness he showed the other day.
"He is so happy and so proud with his effort and determination," added Mourinho, who was impressed by Schweinsteiger's professionalism during his spell out of the team.
"Everybody was happy. I was happy. When he was not training with the team, he did it in a professional way.
"When he started training with the team, he was struggling a bit because it is not easy but he fought against that and managed to do it without injuries and the need to stop. So he was continuously working for a month.
"We felt that it would be a good opportunity for him to play a little bit. He’s another one that can help us and during the season you have injuries and suspensions.
"For example, in that match, Paul Pogba and Marouane Fellaini were both suspended, so two fewer midfield players were available for the match and he was ready.
"Of course, he came on at 3-1 and he came on for a few minutes, but if we needed him before then, he was ready.
"His future is about this. He's another one in the squad working to have more chances."
Mourinho, whose side visit Everton in the Premier League on Sunday looking to narrow a gap between themselves and the top four that could extend to double figures, has praised striker Anthony Martial for his efforts to get back to form after a difficult spell.
The France international scored twice against West Ham, having previously scored only two goals all season.
"He's working. He's working harder than before to be honest," said Mourinho of Martial. "When he scored two, maybe it helped his happiness and confidence levels to be back.
"As an attacking player you can play very well but if you don't score goals, the happiness is not there. I hope that helps him."
Original source: Mourinho offers Schweinsteiger United lifeline