Speculation has suggested that Mourinho could be set to leave Real Madrid at the end of the season, and he has been connected with a number of clubs.
Manchester City has been mooted as a possible destination, with Mourinho regularly hinting that he would like to return to work in English football.
However, Mancini stressed earlier this week that he still had the backing of City's owners despite bowing out of the UEFA Champions League at the group stage for a second straight year.
And the Italian is not feeling threatened by any talk about Mourinho as he remains focused on the task ahead at City.
"I read one day that Mourinho is going to Paris Saint-Germain. The next day it's Inter, then Manchester City, Manchester United and then Chelsea," said Mancini.
"I am very happy for him. I think he is working well in what he is trying to do.
"But I don't feel under any pressure at City. I am disappointed we are out of the Champions League, but this is football."