Spurs are already winless against the La Liga giants after five matches in the both clubs' history, with Spurs suffering three losses and two draws when facing Zinedine Zidane's side.
However, Mauricio Pochettino's men have the chance to finally beat the Champions League holders as they face Real in Group H of the elite competition at Wembley Stadium.
But Matthaus, who played for Bayern Munich and Inter Milan during an illustrious career, claimed that both sides will cancel each other out - predicting the two heavyweights to draw 1-1.
"1-1 will suit both teams. It is the smart play and these are two smart teams, with two smart coaches," Matthaus predicted. "Toni Kroos and Luka Modric are the creative hub and, if you give them time and space, they will kill you.
"For me, that means you can’t defend from the edge of your own box. The press has to start before halfway. It’s vital Spurs put them under pressure early and don’t give them the chance to play those passes into Ronaldo, Benzema and Isco.
"If they are able to make clean passes it’s a real problem for you. If not, it becomes a problem for Real. Spurs must not let them dominate midfield."
Three points for Spurs and they will book their place in the last 16 of the Champions League, as they sit on level seven points with Real while APOEL Nicosia and Borussia Dortmund are fighting for their lives on one point.
It remains to be seen if 24-year-old ace Harry Kane will be included in the Spurs side, after missing Saturday's 1-0 defeat to Manchester United with a hamstring strain. However, Danny Rose could return to the side.