The Switzerland international has been linked with a switch to Old Trafford as Mourinho is desperate for a new centre-back to turn United’s season around.
Akanji recently revealed he is keen on moving to England one day.
However, he says he will not be moving to United as long as Mourinho is still in charge.
“It’s true that from an early age I was a fan of Manchester United,” he told German publication WAZ.
“But at the moment I’m not really looking at the games because I do not like the way they play under Jose Mourinho.”
The 23-year-old moved to Dortmund in the summer from Basel and has impressed as he has helped the German side to a superb start to the season.
Lucien Favre’s side are currently seven points clear at the top of the Bundesliga after 13 games in 2018/19.
They are looking to win the league for the first time since former boss Jurgen Klopp ledf them to the title in 2015/16.
And he insists they need to keep working hard to achieve their goals.
“We’ll see,” Akanji added when asked if they can win the Bundesliga.
“We will do everything we can to get a title this year. Whatever.
“You never know what will come out in the end, but I’ll do anything to win a trophy this year.”
Asked if he plans to leave Germany any time soon, he added: “You can not plan a career.
“There can always be something in between, such as injuries.
“I just try to show the best possible performance in the place where I am.”