Mourinho was speaking at his final Benfica press conference of the season after the club completed the Portuguese Primeira Liga campaign unbeaten but finished third, behind champions Porto and Sporting CP. A season of 11 draws proved costly enough to deny them the title despite going the entire campaign without defeat.
He acknowledged that his agent, Jorge Mendes, has been in discussions at a level beyond what can be dismissed, while drawing a precise distinction between those conversations and a formal approach.
"I have a proposal from Benfica. I don't have a proposal from Real Madrid. At the same time, I was saying that to hide that there is nothing — we cannot do that. There is something, but not with me directly. I need time, I need space, and I think this week is going to be very important."
Mourinho has a clause in his Benfica contract that allows him to leave for a reported 3 million euros within a defined window after the season ends. Real Madrid are understood to have him on a shortlist of three candidates to replace Álvaro Arbeloa, who was appointed interim head coach in January following Xabi Alonso's departure.
He was warm in his assessment of his time in Lisbon, describing it as one of the happiest periods of his managerial career regardless of what follows.
"I was happy every single day here. In my career, even when I won more trophies at other clubs, I was not happy every day. But here at Benfica, with my group, I was happy every day without exception."
Asked whether he could turn down Real Madrid if a formal offer arrived, he declined to give a straight answer.
"If, if, if... Depends on what they expect of me, whether I am in a position to fulfil what they propose. I want time to analyse, think and decide for myself."
Real Madrid president Florentino Pérez praised Mourinho publicly last week in a television interview, saying the Portuguese had increased the club's competitiveness during his previous spell from 2010 to 2013.