The club could still face an 18-point deduction - and instant relegation - if it is decided that SPL rules were breached by UBIG's declaration of insolvency last week. The board met ahead of an all-club meeting, which had already been scheduled to discuss ongoing attempts at league reconstruction.
The board is expected to reconvene after lunchtime when the other club representatives leave. UBIG was listed on a Lithuanian government website of insolvent firms on Thursday after reportedly declaring itself unable to meet its liabilities.
The firm owns about four-fifths of shares in Hearts and SPL rules can lead to points deductions if an owner suffers an insolvency event.
The SPL has been consulting with its lawyers over its rules and whether UBIG's action breaches them. Issues under discussion will include whether UBIG has officially suffered an insolvency event in the Lithuanian courts.
The relationship between UBIG and Hearts will also come into consideration. The club will argue that they have been self-sufficient since early last year so have not benefited from the funding of an insolvent company this season. However, they owe UBIG about £10million of their £25million debt.
Hearts could face action further down the line, with their final 44-point total meaning they would be deducted 15 points next season if they are deemed to fall foul of the insolvency rules at a later date.
Dundee, who were promoted to the SPL after the Rangers newco's application to join the league was rejected last summer, finished bottom of the SPL, 14 points behind Hearts, and they could be handed a reprieve if Hearts are deducted a third of last season's points tally.
On his way into the SPL meeting, Dundee chief executive Scot Gardiner said: "I don't have any thoughts on it at all. It's nothing to do with us until we are told something different.
"It could impact on us but it's nothing to do with us. At the moment we are planning for the SFL. We are trying to sign players to win the First Division and hopefully we will be successful in doing that."