The Scottish Professional Football League say they will work with police and both Kilmarnock and Rangers to determine what action is needed following a pitch invasion at Rugby Park.
Two Danny Johnson penalties saved Dundee from opening day defeat as James McPake's side drew 2-2 at Dunfermline.
The draw of the newly-rebranded Tunnock’s Caramel Wafer Challenge Cup will see an Angus derby in the first round.
Celtic will kick-off their quest for a ninth straight Ladbrokes Premiership title against St Johnstone on August 3.
St Mirren 1-1 Dundee Utd: Tangerines remain in the Championship after heart-breaking shootout defeat
Despite playing in a division below, Dundee United earned almost twice what neighbours Dundee recieved from the £9 million payout this week from the SPFL.
A financial expert has warned Dundee to expect a revenue drop of at least £1.5 million in the Championship next season.
Dundee have been under threat of relegation to the Championship for a long time – now years of poor decisions look certain to have cost them their place at the top table.
It was yet more heartache for Dundee as Sam Cosgrove's double won the day for Aberdeen at Dens Park.
The SPFL post-split fixtures has thrown up a potential barn-storming end to the season – with Dundee to face St Mirren in a final day showdown.
Dundee United have made experienced defender Mark Reynolds' move to Tannadice a permanent arrangement.
St Mirren put major dent in Dundee's Premiership survival hopes by downing the Dee 2-1 in Paisley.
Dundee United head to East End Park in a bid to put pressure on league leaders Ross County.