The Sun claims Wednesday are aware of McCarthy's interest in the role, should it become available.
Its current incumbent, Jos Luhukay, has overseen a run of four successive defeats, yielding an aggregate score of 12-2.
McCarthy is out of work after leaving Ipswich towards the end of last season, after nearly six years in the job.
In that time, the experienced Yorkshireman led the Tractor Boys to a trio of top-half finishes, despite being provided with limited funding, having previously won promotions at Sunderland and Wolverhampton Wanderers.
Many Sheffield Wednesday supporters, including the former England cricket captain Michael Vaughan, have already championed McCarthy's appointment.
But the following Ipswich fans have responded with warnings...
Ohh Michael, I wouldn't wish that on anybody! Especially a club I do kind of like— Scott Fraser (@SFraze_ITFC) November 5, 2018
No Michael, he will ruin your club ,Pol what he did at IPSWICH, boring football lost the fans , he is also rude and foul mouthed,— Nick King (@King66Nick) November 5, 2018
If you like watching functional attritional football that will bore you to tears good luck. Glad #ITFC are shot of him— Rodd (@TheOfficialRodd) November 5, 2018
If you enjoy square pegs in round holes, one up front, and no shots on target along with 25% possession AT HOME, then he's the man! Oh, and don't forget signalling the fans to fuck off when you go one up against your rivals— Steve (@SteveITFC) November 5, 2018
good luck to them, they'll need it.— Caroline Cooper (@carolineitfc) November 4, 2018
Be good to see Mick McCarthy take the Sheffield Wednesday job.— Elder Grizzly (@ElderGrizzly) November 4, 2018
A job with around double the wage budget of #itfc, so his media chums excuses would wear rather thin and their obsession with us should end.
Anything but playoffs would be a failure?
Although not everyone feels that way, it seems...
Depends on size of budget. A few sides got huge budgets and aren’t Wednesday close to FFP issues? We all know MM would have spent more wisely than PH and we wouldn’t be bottom with him in charge. He will do a decent job at Wednesday.— Potter (@potter80) November 4, 2018
Sheffield Wednesday travel to third-place Sheffield United for the season's first Steel City derby on Friday, for a repeat of Luhukay's first game in charge at Hillsborough.
The Dutchman led the Owls to a mid-table finish in difficult circumstances last season, and had them sixth in the Championship just four games ago.
Why would the former Ipswich boss be such bad news for Sheffield Wednesday?