A report in Marca, a Spanish newspaper with traditionally strong links to the club, claimed Mourinho and Perez had agreed the Portuguese would leave the Bernabeu at the end of the season.
But speaking ahead of tonight's Champions League game with Ajax, Mourinho said of the speculation: "Neither I nor the president are going to say a word. My future is tonight, which is my 101st match in the Champions League."
Rumours of discord between him and Perez are not new but Mourinho was adamant their relationship had not changed for the worse, adding: "Ask him. I don't have to tell you what I talk to the president about.
"My relationship with him is good and I've already said that. I'm not going to feed this situation."
Mourinho has come under fire from supporters this season following third-placed Madrid's slow start to the domestic season which has enabled arch-rivals Barcelona to establish an 11-point advantage over the defending Spanish champions.
They are also five points behind second-placed Atletico Madrid despite Saturday night's 2-0 defeat of their near-neighbours.
Mourinho was jeered by sections of the crowd in last Tuesday's Copa del Rey defeat of Alcoyano, prompting the former Porto, Chelsea and Inter Milan boss to offer supporters the chance to vent their frustration by arranging to come to the side of the pitch 40 minutes before the Atletico game.
The reaction was mixed but with less than 5,000 fans inside the Bernabeu at the time, it offered little indication as to how the majority were feeling.
On the gesture, he said: "I went out there because whistling was expected.
"If there's animosity, the best thing is that it comes out before the match and against me personally so later on they can support the team and there won't be an opinion, but support."
Mourinho was, as ever, convincing, but his performance will do little to quell the specu-lation his time in Madrid is coming to an end.
The Marca report claimed: "Jose Mourinho will not coach Real Madrid next season."