Stuttering Real go into the derby eight points behind second-placed Atletico and 11 adrift of arch rivals Barcelona.
Some supporters vented their frustration during Tuesday's Copa del Rey game against third-tier Alcoyano, which Real won 3-0 to progress to the last 16 by 7-1 on aggregate.
"They applaud me, they whistle me, that's life in football," Mourinho said at a news conference on Friday when asked about the reaction of the fans. "I'll go out onto the pitch tomorrow at 9.20 p.m. on my own," he added.
"Those who want to whistle me they can do it. People who come later should support their team, support their Real Madrid so that Real Madrid can achieve its objective which is to win the match.
"It's not a challenge of any kind. If they want to whistle I'll accept it with humility, and with calm as well because I have been around for many years."
Real's poor start to the defence of their La Liga title has prompted speculation Mourinho will not last the season, although success in the Champions League is what really matters to big-spending club president Florentino Perez.
Real are through to the last 16 of Europe's elite club competition as Mourinho, who won the title with Porto in 2004 and Inter Milan in 2010, attempts to secure the 10th European Cup that has eluded the club since 2002.
"For me there is nothing at stake," he said when asked if Saturday's game could decide his future. "You can draw your own conclusions. For me the match is one to enjoy. If you win good, if you lose bad."
Atletico coach Diego Simeone, who has transformed the team since taking over in December 2011, said the derby was a special occasion but getting three points was what mattered most.
Madrid's second club have not beaten Real in more than a decade and Claudio Ranieri was the last Atletico coach to savour victory when former Netherlands striker Jimmy Floyd Hasselbaink scored twice in a 3-1 away triumph in 1999.
"The derby is always fantastic, it's a special game that excites you and you experience in a different way," the former Argentina captain told a news conference on Friday.
"But as we always say, they are three points, not nine, in play," added the 42-year-old.
"We are not going to waste time thinking about the statistics. Just like we have won 16 consecutive games in the Europa League, all streaks come to an end at some point.
"I am just focusing on what we will be facing, a great team, powerful, very strong, globally significant. With our tools and our options we'll try to win as a team."