Jose Mourinho's Real travel to German side Borussia Dortmund on April 24, while Spanish league leaders Barcelona, who edged Paris St-Germain on away goals in the quarter-finals, face new Bundesliga champions Bayern Munich the day before. The second legs are a week later.
Real beat Galatasaray to make the last four despite stuttering to a 3-2 defeat in Istanbul, but McClaren, former England boss, told Sky Sports News: "Real are the favourites. They've got the momentum, the focus and a manager who knows how to win the competition and just knows how to win.
"They also will play at the Bernabeu in the second leg. It will be a very open contest but ultimately Dortmund will be just delighted to have reached this stage.
"Dortmund are the underdogs and that puts them at an advantage - they can just go out and play."
Dortmund, second in the Bundesliga and trailing Bayern Munich by 20 points, needed two late goals to squeeze past Malaga in the quarters.
It is this spirit that has really caught McClaren's eye and the man who picked up the managerial reins of Bundesliga side Wolfsburg in May 2010 said: "They are a terrific fit team. They are strong and playing well and also beat Real earlier in the season.
"They are a smart attacking side and press so high. In transition from defence to attack they are the best team in this competition. That's where Real do have a weakness.
"The Dortmund boss Jürgen Kloppis is crazy but very good! When I first went to Germany he was on TV more often than managing! He's so passionate and he brings that to the team. He carries them forward with energy and passion."
Barca's Lionel Messi and Real's Cristiano Ronaldo continue to be the stand-out performers in the Champions League this season, but they aren't the only stars likely to make the headlines in the semi-finals says McClaren.
The ex-boss at Middlesbrough, FC Twente and Nottingham Forest added: "All four teams have special players and Dortmund striker Robert Lewandowski is one of them.
"When I went to Germany he wasn't even in the team. He has adapted well and now he's the star and in the semi-finals you need your goalscorers.
"Real have Ronaldo. He's that special ingredient that can win you the game and put you into a final - and he's getting better and better. The bigger the stage, the better it is for him. He's the complete player. Nobody speaks badly of him. He's a true professional and that's why he's getting the rewards now."
The prospect of an all-Spanish El Clasico final remains on the cards and although that may be the choice of many neutral supporters, McClaren fears this may not happen.
"Barcelona are fragile - with or without Lionel Messi," he added. "They are especially vulnerable at the back. Bayern are a real threat.
"Real are more of a team than Barcelona. Messi is the first name on their team sheet but do they have an over-reliance on him? I think so. They were out against PSG and he changed everything. He was instrumental in their equaliser.
"Bayern are exceptional. To be 20 points ahead in the Bundesliga is some achievement. Their strength is they are a team - organised and ruthless.
"They are not just one player - all 11 - and they have an experienced coach in Jupp Heynckes. The arrival of Pep Guardiola at the club has set the German league alight.
"The Premier League needs to watch out and Germany have got their reward. They could have one and maybe two teams in the final."