The attacker has failed to make an appearance for United's first-team this term, with Louis van Gaal strengthening his squad over the summer.
As a result, Wednesday reportedly believe he could be made available for loan and they feel he could enhance the squad at Hillsbrough.
The Owls already have a team stacked with quality, but Carlos Carvalhal is keen to add further talent to his current group.
If Lingard does join, he would offer the Championship side even greater competition for the forward places in their starting line-up.
The England youth international is comfortable playing as a striker, but he can also perform a function as a wide-man, with his versatility a big asset.
So far the bulk of Lingard's senior experience has come out on loan - with the 22-year-old having temporary spells at Brighton & Hove Albion and Birmingham City last season.