The judge presiding over Hearts and Partick Thistle's battle to avoid relegation is considering motions to terminate or suspend the case so it can go to arbitration.
A lawyer representing promoted clubs Dundee United, Raith Rovers and Cove Rangers called for the case to be thrown out of the Court of Session while the Scottish Professional Football League representative argued it should be "sisted".
They want Lord Clark to refer the case to an arbitration panel set up by the Scottish Football Association.
However, the petitioners have argued that arbitration could lead to costly delays in settling the case, which began via video link exactly a month before the Scottish Premiership season is scheduled to start.
The pair launched a legal bid to scrap promotion and relegation this season after several attempts at league reconstruction failed to halt them slipping down a division, along with Stranraer, following a vote by clubs on April 15 to curtail the season in the wake of the coronavirus pandemic.
Garry Borland QC, acting for the promoted trio, argued clubs were "contractually obliged" to comply with SPFL rules and Scottish Football Association articles, and that the row was a "football dispute" which required to be settled by arbitration under the latter.
He added that rules stated "members may not take a football dispute to a court of law except with prior approval of the Scottish Football Association board".
Borland argued it was feasible for arbitration to take place in time for the season kick-off and blamed Hearts and Thistle for timing problems given they had waited two months to launch legal action.
He dismissed claims from the two clubs that they had the right to pursue the matter in the courts, including that the case was not technically a "football dispute" as stated in SFA article 99.
"It is obvious that the present dispute arises out of and relates to association football," he said. "The contention of the petitioners to the contrary is fanciful.
"What they are attempting to do is stop relegation and promotion, which has been decided. Promotion and relegation are fundamental parts of football. They are the meat and drink of football."
Gerry Moynihan, the QC for the SPFL, argued arbitration could cut through the "legal noise" and get to the heart of the matter swiftly.
He pointed out that it was a disciplinary matter under SFA rules to raise court proceedings with potential punishments including termination of membership or, "to use a Glasgow expression, you're out the game". He claimed it could even be a disciplinary issue for the promoted clubs and SPFL to continue with the case.
That last claim was described as "fanciful" by David Thomson QC, representing Hearts and Thistle, given the SFA articles only refer to those who "take" action.
In his introductory comments, Thomson claimed attempts in the SFA articles to prevent parties going to court were unlawful and both clubs had done everything to avoid that by pursuing reconstruction.
He claimed the process of setting up an arbitration panel by identifying, nominating and checking the availability of panellists would inevitably lead to a delay given there were two 14-day periods associated with the procedure.
"The court can deal with this," he added. "The alternative is to go down a route which has not commenced yet."
He claimed it was "surprising" to hear his opponents argue that the case was best left to football authorities given that an arbitration panel would be made up of retired sheriffs for example.
The hearing will continue at 2pm on Thursday.
