Mourinho, imo, will be after the CL first, FA Cup 2nd & top 4, 3rd, if he concludes the title is over (which is another point or so away).
He doesn't give a fuck about staying at Utd, just his own success. Similar Conte. He might walk anyway in May. Pochettino probably has no qualms about moving on, maybe to the swamp. Klopp is DESPERATE for any kind of trophy.
Then there are the players, who all want to win stuff, not come 3rd.
Wenger wants top 4, but even they usually start their run at the end.