Speculation had suggested that the Owls were plotting an approach for the Scotland international.
It remains to be seen whether Bardsley will figure in Paolo Di Canio's plans next season, with Sunderland in the midst of a summer rebuilding programme.
Wednesday were said to hold an interest, with Bardsley a seasoned campaigner who would add considerable experience to their ranks.
Jones is, however, happy with his current options at full-back.
He already has Lewis Buxton and Kieran Lee as contenders at right-back, while Joe Mattock and Rafael Floro offer competition on the left.
When pressed on whether there is any substance to the Bardsley rumours, Jones said in the Sheffield Star: "No. I don't need a full-back. I've got Lewis and Lee."