Blades had Coady on loan as a youngster, while he was at Liverpool, and his performances at Brammal Lane impressed.
With Chris Wilder’s side now looking to adjust to life at Championship level, following promotion this season, Coady has come back to the Yorkshire side’s wishlist.
Sheffield United have already had one approach turned down for the 24-year-old this summer, with Wolves insisting that Coady isn’t for sale.
However, the Sheffield Star claims that Wilder believes he can get a deal over the line for the versatile player, who can cover at centre-back or in midfield.
Coady has just 12 months remaining on his deal at Wolves, so this could be Nuno’s side’s last chance to receive a significant fee for the ex-Liverpool man.
Coady has started in both of Wolves’ first two Championship matches this season, with Nuno’s men beating both Middlesbrough and Derby County.