The two European heavyweights go head-to-head in the first leg of their eagerly-awaited UEFA Champions League last-16 tie, with the return leg at Old Trafford on 5 March.
While Pepe acknowledges this season's runaway Premier League leaders will be tough to beat, he insists they are not invincible.
He said: "United are the leaders in England and are having a good season but they not are invincible. This Real team could beat Manchester United.
"Wayne Rooney and Robin van Persie are the key men but we know how to stop these players. The Real squad has experience and we are able to plan for this type of match.
"Van Persie is in a big moment but not is easy to score goals against us.
"There is not a clear favourite because any goal could change the picture. Our objective is to obtain a good scoreline in the Bernabeu and to fly to Old Trafford with more calm.
"But I am convinced that the round will be decided in England."
You can only watch the best UEFA Champions League coverage here on Sky Sports. Watch Real Madrid v Manchester United exclusively live on Sky Sports 2HD and Sky Go from 6:00pm on Wednesday 13th February. Click here for more details and watch goals from United's route to the last 16.