The Switzerland international was linked with the Red Devils during the January transfer window, but ended up completing a €22 million (£19m/$25m) switch to Germany .
The 23-year-old has impressed in the Bundesliga and is considered to have another big-money move in him at some stage.
He told Bluewin : "Many know that Manchester United has been my favourite club since childhood. It would be nice to play there, but that's not an issue right now.
"I am very satisfied in Dortmund. I want to win titles with BVB and compete in many more big tournaments with the Swiss national team."
United remain in the market for defensive additions after failing to bolster their ranks in that department over the summer.
Akanji may be a solution to those problems, but prising him out of a four-and-a-half-year contract at Dortmund will be difficult at this stage.
That is likely to force Jose Mourinho to look elsewhere, with any move for a Swiss star having to be put on hold as he chases down other targets in Germany.
“I always want to go higher, as far as possible,” added Akanji.
“But planning the future is difficult. You never know what will happen.
“The most important thing is to stay healthy. The short-term goal for the club is to consolidate in the Champions League and to continue playing well in the Bundesliga.
“There will be setbacks along the way. Life does not always go upwards, but also downwards, not just in football. I will try to be a good person on and off the field.”