The report claims the Owls will pay Norwich City a £500,000 loan fee, and cover all of his £32,000 per week wages.
The former Celtic striker has experience playing in the Championship, making 16 starts for Norwich last season.
He also made 16 appearances off the bench, scoring 12 goals in total and providing six assists.
In the opening two games of the Premier League season Hooper has played a total of 10 minutes out of a possible 180.
The Sun's report states Sheffield Wednesday are the only club willing to stump up the loan fee and pay his wages in full.
An editorial in the Sheffield Telegraph this week commented that a striker is the missing piece in the puzzle at Wednesday, after largely impressive summer transfer window.
New owner Dejphon Chansiri has invested well, and while a deal to sign Hooper permanently may be preferable, if it does not work out at least they are not committed.
The Owls have four points from their opening nine games and face Yorkshire rivals Leeds United at Elland Road this lunchtime.