Mulvey, who led the club to the A-League championship in 2014, is suing the club over unpaid wages and Gambaro Hotel and Restaurant is seeking to have the club wound up for alleged unpaid debts, the Courier-Mail reported.
Mulvey, sacked by Roar in November last year, has launched District Court action claiming wages, damages and costs of an overall amount still to be assessed.
Gambaro Pty Ltd has filed a Supreme Court application to wind up Roar over an alleged June debt of $30,424 that's yet to be paid.
The application is listed for a directions hearing on 16 September.
Similar action has been taken by the Queensland Rugby Union, which wanted Roar wound up over more than $60,000 of unpaid Ballymore tenancy rent.
The scheduled court date of 19 August was avoided when the club settled the debt the day before.
Interim Roar chief executive officer David Pourre declined to comment.
Roar's Indonesian owner, the Bakrie Group, have been put on notice by Football Federation Australia, which has threatened to strip it of its A-League licence if it does do not come up with a genuine plan to pay off the club's debts and make it viable again.