Lyon eliminated Real, the nine-time champions, at the same stage of last season's Champions League and have yet to taste defeat at the hands of the Spanish giants in six encounters in the competition.
Mourinho, however, has tasted Champions League success with Porto and Inter Milan, who he led to glory last season, and says Real's rich pedigree means they should not fear anyone.
"They're tough opponents, who know how to play this kind of match, but we are Real Madrid," said Mourinho at the pre-game press conference.
"The statistics are against us but they are figures from the past.
"If we think it'll be easy, we'll be in trouble. But we don't think that. If we believe that everything will be decided tomorrow (Tuesday), we'll be in trouble. But we don't believe that."
He added: "We are ready and convinced of our qualities. We're not attached to the past and we respect our opponents for what they are today.
"But we are Real Madrid, the champion of champions of European football. There's pressure but also conviction that accompanies us."
Despite Real having fallen to Lyon in the last 16 last season, Mourinho said he had placed no special emphasis on his team's psychological readiness and emphasised the changes that the Real squad had undergone since.
"There are lots of new players who have joined the squad and weren't here for the elimination last year," he said.
"Me and Ricardo (Carvalho) eliminated them (Lyon) with Porto. Cristiano Ronaldo scored against them with Manchester United (in 2008). There are no negative aspects."
Real habitually deploy a counter-attacking 4-2-3-1 formation in domestic games but Mourinho has been known to stiffen his midfield by fielding an extra central midfielder in European away games.
He refused to be drawn, however, on his tactical plan for taking on Claude Puel's team and would not confirm whether or not former Lyon striker Karim Benzema would start the match.
"You'd like to know (if Benzema will play), but Puel would like to know too," said the Portuguese.
"Contrary to my usual habits, I'm not open to talking about that kind of thing. We're not going to talk about either Karim or (Emmanuel) Adebayor.
"We're not going to talk about three midfielders either. You can try (to ask) but my lips will remain sealed. I'm the only one who knows who's going to play."