Actually, Mourinho didn't just leave on his own. When he left,
so did the following people.
Baltemar Brito (assistant manager/coach), Rui Faria (assistant
manager/fitness coach) Andre Villas (head opposition scout/first
team coach) and Silvino Louro (assistant manager/goalkeeper
coach).
On top of finding a new manager, Chelsea has to look to fill all
these positions as well. Even if they get people in, it takes time
to build up a good and effective working relationship.