The Owls have been in administration since October after 10 years under the ownership of Dejphon Chansiri.
They were relegated from the Championship on Sunday following a 2-1 defeat at city rivals Sheffield United. It was the earliest-ever relegation in English football.
Administrators Begbies Traynor chose the Bord group after it paid a non-refundable deposit of £2.5m.
It has been funding the club’s losses since then to the tune of about £1m a month.
The trio have been going through the owners and directors’ test with the EFL and the new Independent Football Regulator since then.
A further payment was due this week to extend the preferred bidder status by a further two weeks.
But the group has pulled out because the club’s valuation is now considered to be lower than the £47.8m originally offered and the consortium are unable to negotiate down, as per the terms of their agreement.
It leaves administrators needing to find another buyer.
In a statement, Sheffield Wednesday’s joint administrators said: “The withdrawal of this bidder does not mean we are returning to the beginning of the process.
“We have already been contacted by other parties who previously participated in the sales process and who have reiterated their interest in acquiring the club.
“We are therefore moving immediately to re-engage with those bidders under a new expedited timetable.”
Adding that the focus on getting the club out of administration and securing its long-term future remains in place, it continued: “We understand that this news will be disappointing and frustrating for supporters.
“However, the club remains operational, funded for the remainder of the season, and interest in the acquisition remains active.”
BBC Sport understands the Bord bid was significantly higher than any other interested parties – and that no other bid matched the requirement for 25p in the pound for creditors.
If the new owners do not pay 25p in the pound, the EFL’s insolvency policy states the club must start the following season with a 15-point deduction.
The Owls have already been docked 18 points this season for financial infringements under Chansiri.
Former Crystal Palace owner Simon Jordan, who at one stage was involved in a consortium which was considering a bid, says that automatic 15-point penalty should be challenged.
On Tuesday, another consortium led by American businessman David Storch stated it was still interested.
“We remain incredibly passionate about the opportunity at Sheffield Wednesday and seeing the club return to its former glory,” the statement read.
“We wish the preferred bidder well through the process but are ready to step in should the opportunity present itself again.
“We know all are disappointed by relegation yet wish the team well as they finish the current season.”
