The Owls had been linked with a move for the German striker, who's left Darmstadt.
Former Darmstadt striker Sandro Wagner
Bild later reported that Bayern Munich could rival the Owls for the 28-year-old, who scored twice against England in the 2009 Euro Under-21 Championship.
Sandro Wagner scores against England for Germany Under-21s
However, Wagner has joined Hoffenheim instead, signing a three-year deal at the Wirsol Rhein-Neckar-Arena.
Wednesday, who've been linked with an £11.5 million bid for Fulham's Ross McCormack in the last 24 hours, made their first signing of the summer on Friday in Steven Fletcher.
Former Sunderland striker Fletcher becomes the Owls' first summer signing
The 29-year-old has agreed a four-year deal at Hillsborough following his release by Sunderland at the end of the campaign.
The Owls, who lost the play-off final last season, were in desperate need for attacking reinforcements this summer, with their four front men combining to score 37 league goals in 2015-16 - with 28 of those attributed to Gary Hooper and Fernando Forestieri.