I don't know if they have inside info, or if they can deduce what's going on by analysing any unusual betting patterns.
But if Nuno is the favourite for the job, and they put him at 12/1, that is NOT self preservation. If they kept giving 12/1 odds on events that are likely to happen, they would become financially bankrupt very quickly.
So I think it is a fair conclusion that Nuno is no longer favourite for the job, as BBC reported last week.
Betting odds for managers are sometimes useful and sometimes not.
It's certainly not useful when trying to ascertain who IS favourite for the position. For example, SkyBet could put Martinez at 1/5 now, and even if they are wrong about him being appointed, they would barely lose any money.