The 30-year-old spent last season on loan with the Championship club.
The defender is attracting plenty of attention from several teams in the Championship, the Star reports, but it is the Owls that he looks set to join.
The 30-year-old is about to begin the final year of his contract at Vicarage Road, and the Star claims that the two clubs are close to reaching a deal regarding the size of the fee.
If Carlos Carvalhal is able to sign Pudil, it will be a major boost to Wednesday's promotion hopes. The Czech Republic international spent last season on loan with the club, and played an important role in helping the Owls reach the play-off final, where they narrowly missed out on going up.
Sheffield Wednesday manager Carlos Carvalhal
With both Pudil and his understudy for the second half of season, Joe Bennett only on loan with Wednesday, Carvalhal would have surely put signing a left-back very near the top of his list of priorities.
And with Pudil having an understanding of how the Owls play, he is arguably the ideal signing in that position as the side look to go one better this year.