Mourinho, 63, led Benfica to an unbeaten season in the Portuguese top flight this season to finish third and has emerged as the leading candidate to replace Real coach Alvaro Arbeloa, according to Spanish and Portuguese media.
Mourinho, who won a La Liga title and Copa del Rey during his previous three-year spell at Real, is under contract at Benfica until June 2027, and he said the Portuguese club has already proposed a renewal.
"My future should be decided this week," Mourinho told reporters on Saturday.
"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, I need time to make my decision, and this week I think is going to be very important."
Arbeloa, speaking ahead of Real's La Liga clash with Sevilla, praised Mourinho and welcomed the prospect of his return to the club, where he coached from 2010 to 2013.
"For me, as one of his players, but above all as a Real Madrid fan, I feel he's number one, and I think he is number one," Arbeloa said on Saturday.
"And I think I felt that way a month ago and I'll continue to feel that Jose has been, is and always will be one of us, and if he's the one here next season, I'll be very happy to see him back home."
Mourinho has previously coached Chelsea, Inter, Manchester United and Tottenham Hotspur, and has also lifted the Champions League trophy twice in his career.