Borussia Dortmund winger Sancho has been a long-term target for United.
Lingard has performed well on loan at West Ham United since January.
If opportunities are not available for Lingard at Old Trafford, the 28-year-old will likely seek a permanent exit from his boyhood club.
Dortmund rate Lingard highly, and according to The Sun, United are hoping to use their interest in a deal for Sancho.
The German club are believed to want £100m for Sancho, but that amount could be reduced with Lingard included in negotiations.