The 20-time English champions have agreed a £73m deal with BVB for the transfer of the England international, who has already agreed personal terms and undergone a medical.
Man United are yet to make an official announcement on the 21-year-old, but Solskjaer has suggested that the move will be confirmed towards the start of next week.
"From what I understand only paperwork, small little details, hopefully we can announce something," the Manchester Evening News quotes Solskjaer as saying. "Let's get all the paperwork done and get him over the line and then I can say what I truly feel about the player."
Sancho, who has spent the last four years in Germany with Dortmund, is still on holiday following his involvement for England at Euro 2020. body check tags ::