"I don't spend one second of my day thinking about it. It looks like you [the media] want to put a lot of pressure on me in relation to that.
"What I would like to understand is why some people can be so excited and happy with the perspective of somebody losing his job. It's sad.
"The Brendan [Rodgers] situation [at Liverpool], he was almost winning the Premier League. He was the Manager of the Year and suddenly people were really happy and working hard until he was sacked. It's strange. I don't belong to this world. I'm too emotional. I hate people losing jobs. Not in football, but in everything."
Mourinho said his only concern was reviving Chelsea, who saw their League Cup defence end in a penalty shootout defeat at Stoke on Wednesday.
The three matches before November's international break could be key, with Liverpool's visit to Stamford Bridge followed by a Champions League clash with Dynamo Kiev and a Premier League trip to Stoke.
"I am worried about the results. I am worried about winning on Saturday," Mourinho added.
It was put to Mourinho that bookmakers are already providing odds on his successor, but he said: "Don't speak with me about bets and odds. It's something that belongs to your culture, not to mine."
Abramovich has sacked seven managers over the course of his 12-year reign at Stamford Bridge, and Mourinho famously left the club in 2007 amid reports of a rift with the owner.