The cost of paying Mourinho out is probably about the same as the lost revenue from a season out of the Champions League.
They break even or double up on those losses now if they bring a new manager in, based on whether that person can effect a turnaround that would at a minimum require closing the eleven point gap to fourth.
And the longer they wait and languish, the more incentive to sack Mourinho and the harder the job for whoever is appointed.
Secondary issues are the possibility Mourinho has alienated the most valuable player in the dressing room, and the huge setback to the stated desire of the club to move away from constant transition and towards a more stable, prudent and inexpensive way of operating.
It's all quite delightful.