Hearts owner Ann Budge has rejected takeover proposals for the club, report the Daily Mail.
Barnsley chief Paul Conway is keen to invest in a Scottish side having failed to do so in Partick Thistle last year due to regulations surrounding dual ownership.
With those set to be relaxed the American businessman has made moves to increase his football investment, with a stake in Barnsley and Swiss side FC Thun, the former club of ex-Hearts defender Jose Goncalves.
Conway revealed that he is open to talking to Scottish clubs, especially during the current situation where finances may be in a precarious position.
Both Hearts and Motherwell have been approached, with the latter also expected to reject any advances.
Budge told the Daily Mail: “I did receive a call from Paul and indeed over recent months I have received similar calls from a number of other would-be investors.
“In line with my contractual commitment to the fans to transfer ownership of Hearts to them, other than informing the Hearts board of the approaches, I have pursued none of them.”
Hearts and Barnsley, of course, were involved in a compensation wrangle earlier this season regarding Daniel Stendel who was manager of the Tykes at the start of the campaign.