I think Chelsea should go against the usual way of this business and actually hold on to the manager. He's one of the best in the business, he's proven that. You're most likely not gonna get a better guy than him since I believe Pep will stay at Bayern for another year or two.
Aside of that, holding on to Mourinho would give him a vote of confidence and hold the players, who are seriously underperforming, accountable. In the Chelsea matches I've seen, it wasn't so much the opponent outsmarting them with clever tactics, but rather players not putting the effort in, committing massive individual errors and thus costing them goals and games.
In today's business, far too many managers are sacked too quickly before the players get held accountable.