However, BBC reporter David Ornstein admits it is 50/50 that a transfer actually materialises.
Sancho continues to impress in the Bundesliga, which has led to a number of European sides taking an interest.
But United are the only English side currently interested in the 18-year-old.
Sancho is said to be uncertain over whether to leave Dortmund this summer - but the Red Devils have a good chance of landing him should he opt to jump ship.
"The big one which not people have spoken about is Jadon Sancho," Ornstein told BBC 5 Live.
"Now Jadon Sancho is among the top targets at Manchester United I understand.
"And Manchester United would be his preferred option if he was to come back and return to the Premier League during this transfer window.
"I'm told that a couple of months this was looking like it would be nailed on.
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"However, he [Sancho] is reluctant to give up Champions League football.
"He is reluctant to join an unstable club. He wants stability and he wants to win things.
"I'm told 'never say never but as things stand it's 50/50 on that one'.
"PSG, Juventus, Real Madrid and Barcelona have also shown firm interest in him.
"But there's been no other interest from Premier League clubs.
"He won't move for the sake of it, it has to be right for him and the fee this summer would be in excess of £100m."
Last week reports suggested Sancho was ready to snub any offers from the Premier League in favour of staying at Dortmund for at least another season.