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 £30m 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.
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.”