The Belgian international featured in his country's 2-0 win over Iceland in the UEFA Nations League earlier this month, as Manchester United manager Jose Mourinho watched on.
According to 'ESPN', Mourinho had originally travelled to keep an eye on Romelu Lukaku, but when the striker was ruled out with a hamstring issue, the Portuguese stayed to see Witsel in action.
Axel Witsel, 29, has played in Portugal, Russia and China in recent years but has long been linked with a move to the Premier League.
Manchester United are said to be targeting a central midfielder, with new £52m signing Fred seemingly out-of-favour and Ander Herrera thought to be angling for a move back to Spain.
Witsel and Dortmund sit top of the Bundesliga, and the 'Red Devils' could be forced to wait until the summer to enter into negotiations over the player.