The Owls are believed to have been trailing Mulgrew for a year, since the Scotland international left previous club Celtic, where he played with current Hillsborough pair Glenn Loovens and Gary Hooper.
And given Blackburn's relegation to League One, after a season in which the 31-year-old missed 18 games, it would appear as though Wednesday have sensed a bargain.
But Blackburn, it seems, will be no pushovers, with their manager Tony Mowbray already admitting his side do not have to offload any more of their star players, after Connor Mahoney and Jason Steele were prised away by Bournemouth and Sunderland respectively.
And Rovers fans have warned the Owls it will take a significantly higher offer to get Mulgrew out of Ewood Park.
Here's what they have been saying about Wednesday's alleged bid on social media...
So. #swfc think mulgrew is worth 200k. he ain't going nowhere.— Danny Edwards ⚪ (@dannybrfc) 28 July 2017
200,000 for Mulgrew is unbelievable. Get real lads.— Upton (@Joshua_Upton) 28 July 2017
To see that Sheffield Wednesday bid 100k rising to 200k for Mulgrew is an insult #Rovers— RoversChat ✍⚪️ (@rovers_chat) 28 July 2017
I wouldn't even sell Mulgrew for £1m rising to £2m. 100k rising to 200k? Sheff Wed that is a joke bid. #rovers— Rick (@RiccyB) 28 July 2017
How much should SheffIeld Wednesday offer for Blackburn's Charlie Mulgrew?