The Sheffield Star reports that McClaren - who has had little success since winning the league with FC Twente seven years ago - spoke to Owls chairman Dejphon Chansiri earlier this week.
And while there is no suggestion the 56-year-old will be offered the chance to succeed Carlos Carvalhal at Hillsborough, the chance to rib their rivals is one which Sheffield United supporters were never going to miss.
Here's what they are saying on Twitter...
It doesn’t stop does it......— Maxydee (@MaxydeeMax) 28 December 2017
Carlos the Clown
.........and here comes the punchline.........Steve McClaren!!
I mean come on #swfc
When are you going to stop all this mucking about #twitterblades
McClaren - who had notable spells as manager of England, Newcastle United and Wolfsburg - was sacked by Derby County in March after a disappointing second spell there, and spent the past few months working as Maccabi Tel Aviv's coaching consultant.
Should the 56-year-old take over at Sheffield Wednesday, one of his first games in charge would be against Sheffield United at Bramall Lane on Friday 12th January.
Would McClaren be a better appointment for Wednesday than Carvalhal was?