Businessman Geoff Sheard has held talks with ex-Sheffield Wednesday chairman Dave Allen about buying his stake in the club, reports BBC Radio Sheffield.
Sheard, who heads a consortium wanting to take over the Owls, described the talks as "very constructive".
In February, Allen said he would sell his stake of almost 11% providing the Owls' supporters' society Wednesdayite, also sell their stake.
The Lancashire-based Sheard would not comment further on the meeting.
Sheard met Wednesdayite, who hold a 10% stake in the club, back in April.
Sheard has also held previous discussions with Sheffield Wednesday director Geoff Hulley and former board member Keith Addy who each own 10% of the club's shareholding.
Last month the club appointed a financial services firm to seek much-needed new investment.
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