The stricken Irn-Bru First Division club were granted interim administration last week in a bid to stave off a winding-up order launched by Her Majesty's Revenue and Customs.
Dunfermline owe the taxman £134,000 and also have further debts worth around £8.5million outstanding to majority shareholder Gavin Masterton and other companies but by entering into administration, the Fife club now face an SFL points penalty.
Administrator Bryan Jackson has already pleaded for leniency, claiming a severe punishment could impede his ability to save the club.
Longmuir, however, stressed he would discuss the matter with the experienced trouble-shooter from accountants PKF before initiating the disciplinary procedures.
He said: "I was speaking to Bryan Jackson this morning and I will be meeting him tomorrow to discuss the plans that he has and how he sees the future of Dunfermline. That actually is the most important issue facing the league.
"We need to be able to manage that situation, as we have managed all the other unfortunate insolvency issues we have had.
"I will be meeting Bryan to try and assess the situation before we do anything. I have given him time to try to see what's happening at Dunfermline. I've been in contact with all the key players within the club, I know what's going on and the SFL will deal with that in the next few days.
"That process of deciding penalties will commence after I meet Bryan tomorrow. It's only fair that I have given him some time to assess the situation before the football authorities come in and do whatever we have got to do. But we have a tried-and-tested process on that one and we have always handled it fairly and have always treated each case on its merits. We will do that again.
"A board meeting will be required and as soon as I speak to Bryan tomorrow, I will have a better understanding of his time scales, what has to be done and we will initiate our process immediately following that."