28-year-old Lingard recaptured some terrific form during a six-month loan spell at West Ham.
The Hammers are keen to make the deal permanent but must now wait for United to purchase Sancho, per the Evening Standard.
United have submitted two bids for the England winger this summer, the latest of which was worth £72m.
It is generally accepted that United will get the deal done, it is just a matter of when.
Dortmund want Sancho sold before their July 23 preseason training camp.
Lingard is expected to start preseason with United, but they could all change if Sancho is signed before then.