The defender spent this past season on loan with the Championship club.
The 30-year-old joined the Owls on loan ahead of this past campaign, and went on to establish himself as a key member of Carlos Carvalhal's side, helping them reach the Championship play-off final.
His form during the season saw Wednesday attempt to bring the Czech Republic international to Hillsborough on a permanent deal during the January transfer window, only for the two sides to fail to reach an agreement regarding a fee, according to the Star.
And while the Star suggests that the Owls are still keen to bring him back to the club, they claim that the fee could once again prove to be a stumbling block with the Yorkshire side reportedly unwilling to meet the asking price.
With the Star adding that Pudil has just one year left on his current deal at Vicarage Road, and given the full-back's age, it is perhaps a steep price to pay.
Nevertheless, he was undoubtedly one of the most consistent performers in the squad that came so close to sealing promotion to the Premier League.
And Carvalhal may ultimately decide that the asking price is an acceptable amount to part with given the contribution that Pudil made during his time on loan.