I don't think Roman can afford to sack him (and I'm not speaking economically). He's going back to the Chelsea Pitch Owners to ask them to sell back the freehold to the club, and he needs to be on their good side. The CPO are almost exclusively hardcore fans, and almost all of them support Mourinho way more than they support Abramovich.
I suspect this is the main reason Jose still has a job. Forget about Chelsea "supporting the manager who won them the league". It didn't stop them from sacking a better coach in Ancelotti and it wouldn't have stopped them now. Mourinho is just a pawn in a bigger game.