The 20-year-old has emerged as arguably the most coveted player in world football having scored 31 goals and created 42 in 90 first-team appearances for Dortmund, including 17 goals and 19 assists in just 35 outings this season.
While every big club wants Sancho in their squad, those who could actually afford him is a smaller group, with Dortmund likely to demand a fee of at least £100m and perhaps as much as £120m.
Manchester City, where he came through the ranks, Real Madrid, Barcelona, Liverpool and Chelsea have all been linked to the England international, but it is Manchester United who are thought to be leading the race as things stand.
Here, Sports Mole looks at which shirt numbers would be available to him if he did move to Old Trafford.
Sancho's favoured shirt number is clear - the number seven he has worn throughout his prodigious Borussia Dortmund first-team career to date, and also his most recent international number.
The only hurdle to him being bestowed the same number at Old Trafford is Alexis Sanchez, who is currently on loan at Inter Milan and due to return to United at the end of the season as things stand.
It is fair to say that Sanchez has not done the famed seven justice since inheriting it from fellow United flop Memphis Depay, though, and with the Red Devils expected to try to offload the Chilean on a permanent basis this season, it should become available for Sancho.
Indeed, given the potential of Sancho and the lack of impact Sanchez has made so far, Ole Gunnar Solskjaer could let the Englishman have his pick even if Sanchez does not leave the club.
It remains to be seen whether the shirt will weigh heavy on the England international's shoulders as it has done for its last three occupants in Sanchez, Depay and Angel Di Maria, but everything suggests that he could be the man to restore the number seven's reputation at Old Trafford.
Another option often associated with wingers is the number 11 shirt, which is currently vacant at United since Anthony Martial switched to number nine.