As per The Star, the Owls are doing so as uncertainty grows regarding Massimo Luongo’s Hillsborough future, with a new deal yet to be agreed with the Australian.
Negotiations are said to be taking place with the 28-year-old, who is entering the final week of his Bluebirds’ contract.
If Sheffield Wednesday do want to secure Vaulks’ signature, though, they face tough competition to do so.
It has previously been reported that QPR, Stoke City and Luton have all been eyeing a move for the Cardiff City man if he departs the Welsh capital this summer.
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Vaulks was a regular for Cardiff in the Championship last campaign, appearing 40 times for them across the league, FA Cup and EFL Cup.
Throughout his time in the Welsh capital, the central midfielder has appeared 117 times for the Bluebirds.
With Massimo Luongo seemingly heading for the exit door, Sheffield Wednesday should now go all in for Will Vaulks.
If they can beat a host of Championship clubs to his signature it will represent a big coup for the club and be a testament to the pull Sheffield Wednesday still have despite being in League One.
Just like Barry Bannan has done, you feel that Vaulks would look a class above in the third-tier.
Indeed, Vaulks, Bannan and Byers could form a formidable midfield trio for the Owls next campaign if the 28-year-old signs on the dotted line at Hillsborough.