Terry Butcher was dismissed at a meeting early last week and it is understood that Dempster will be joined by another board member to speak to potential candidates.
However, Rod Petrie will not be involved. The unpopular Hibs chairman has been the subject of protests from supporters and is not expected to be present during the interviews this week.
Dempster intends to have the new manager in place in time for the start of pre-season training, with Ian Murray - the former Hibs captain and now manager of Dumbarton - among the favourites to be appointed. Danny Lennon, the erstwhile manager at St Mirren, and Motherwell manager Stuart McCall have also been linked with the vacancy.
Finding a new manager is now the primary concern for Dempster, who last week appointed former Falkirk managing director George Craig as the new head of football operations. Dempster has acknowledged that she will now work closely with Craig to produce written plans on the way forward for Hibs.
"Myself and George will be developing and writing both football and non-football plans for the club," said Dempster. "While these will be internal club documents, it is positive that supporters should have an understanding of what we are going to do.
"Starting from grass roots, we need to get more kids playing football in Hibernian strips. Apart from getting youngsters more active it has two big effects - it creates a bigger talent pool for us to choose from and it also creates Hibernian supporters of the future.
"We also have to improve our player identification and recruitment at academy level. We need a more structured recruitment plan, particularly in our area. It is not acceptable to lose out on local boys leaving to go to other Scottish clubs or beyond."