The Mail report Alex Neil is ready to sanction a deal, despite letting Lewis Grabban join Bournemouth yesterday.
This is because the Canaries remain hopeful of signing Steven Naismith from Everton, with such a move almost entirely funded by cashing in on Grabban.
The report reads: "Norwich boss Alex Neil is also prepared to sell Gary Hooper to Sheffield Wednesday as he hopes to complete an £8million deal for Everton's Steven Naismith."
Hooper has been surplus to requirements at Norwich since Neil took over earlier this year, and was loaned to Wednesday earlier on this season.
He is yet to really get going at Hillsborough, scoring two goals in 10 appearances, four of which have been starts.
Getting the former Celtic man signed up permanently is the minimum requirement for the Owls this January, but he may not be the only striker they sign this month as they seek to set themselves up to kick on and make the play-offs.