The midfielder has agreed to join the Bundesliga side in a €20 million (£18m/$23m) move this summer after just one season in China.
And transfer broker Stefani has revealed that the midfielder had his choice of top leagues in Europe once his low release clause and desire to leave Tianjin was revealed.
However, he steered him away from joining Jose Mourinho's side after the Premier League side showed an interest.
"I remembered that a few months earlier I had been to Dortmund, where I met someone from the club. I call that man and he brings me into contact with the management.
"Sports director Michael Zorc and CEO Hans-Joachim Watzke invited me to come and talk at a time when Axel was at the World Cup in Russia. There I heard that Dortmund were looking for a player like Witsel.
"I explained to them that the Portuguese lawyer of Witsel has negotiated a buy-out clause of €20m with Tianjin. That sounded like music to them, because they thought that Tianjin would ask for an amount of around €60m for Axel. When the transfer later started rolling, the Chinese still tried to get out of that buyout clause, but it was conclusive.
"There were other candidates. Manchester United wanted him, Napoli too. But I told Axel: 'At Dortmund you are the number one, at Manchester you are one of the many... and at Napoli too'."
But Witsel was not the only midfielder United were chasing, according to Stefani, who says they also had Chelsea star N'Golo Kante high on their shortlist.
"I know from a very good source that Mourinho said he wanted Witsel, but not in the first place. N'Golo Kante topped his list. Eventually Axel said: 'Do me a favour and finish it as quickly as possible, because I really want to go to Dortmund'."
Stefani has been involved in several big deals involving Belgian players and was delighted to help organise another one during a summer in which Eden Hazard and Thibaut Courtois are the Belgians who have dominated the headlines.
"The entire transfer from Axel Witsel has been like a fairy tale. If someone had told me four months ago that I would arrange the transfer from Witsel to Dortmund, I would have said it's is impossible!
"Look around ... Courtois, nothing yet. Hazard, nothing. Alderweireld, nothing. And who is the first one? Axel Witsel. Without problems, he did not have to skip training or anything to force a move" he laughed.