It comes after a BBC Sheffield report suggested Wednesday had been in contact with his representatives over a possible move, though reports from South Wales intimated that while he has an appreciation for the heritage of the club, his preference would be to find employment in the Championship.
Those reports stressed Vaulks has a number of options heading into the summer. He has been of interest to the Owls previously.
The 28-year-old is one of eight senior players to have been confirmed to be leaving Cardiff as manager Steve Morison continues a changing room turnover at the club. Other names include former Owls centre-half Aden Flint and one-time Owls transfer target Josh Murphy.
Wednesday are looking to revamp their squad following the release of three senior players and the return of their vast loan cohort to their parent clubs.
The futures of four players – Nathaniel Mendez-Laing, Jack Hunt, Joe Wildsmith and Massimo Luongo – are yet to be confirmed as their contracts rapidly approach their end.
The latest player to have been linked with a move to Wednesday is veteran Wycombe Wanderers goalkeeper David Stockdale, who like Vaulks would be available for a free transfer.