Hearts and Motherwell have declined an approach from Barnsley co-chairman Paul Conway for takeover talks.
The American businessman made contact with the Scottish Premiership clubs after doing likewise with Partick Thistle last year.
However, both clubs rejected the offer of discussing a buy-out.
Motherwell are the division's only fan-owned club, with Foundation of Hearts set for a controlling share of the Tynecastle outfit this year.
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Hearts owner Ann Budge was due to transfer her majority stake to the supporters group next month, but that has been postponed because of the uncertainty caused by the coronavirus shutdown.
Last week, Budge spoke to staff about taking a 50% wage cut, and reiterated on Thursday the need for a reduction in pay if the club are to survive the next six months without playing games.
Motherwell, owned by the Well Society, have no external debt with chief executive Alan Burrows telling BBC Scotland last week that there are no plans yet to follow Hearts' approach.