It is claimed that Wednesday's offer could have eventually risen to £200,000, depending on certain clauses being met.
Blackburn's Charlie Mulgrew (second left)
The Owls are looking to strengthen their options at centre-back, with Tom Lees and Glenn Loovens their only recognised senior players in that position.
However, they have so far been frustrated in their attempts to do so, with head coach Carlos Carvalhal blaming inflated price tags.
And it appears as though Wednesday were trying to snag a bargain with Mulgrew, who was relegated to League One with Blackburn last season.
The Owls were initially linked with a move for the former Celtic captain upon his release by the Bhoys a year ago, before their interest resurfaced earlier this month.
Charlie Mulgrew (left) with Gary Hooper (right) at Celtic
The 31-year-old, who is a former clubmate of Hillsborough pair Gary Hooper and Loovens, can also operate as a left-back or central midfielder.
Should Sheffield Wednesday up their bid for Blackburn Rovers' Charlie Mulgrew?