City face a last 16 second leg decider against the Spanish giants at the Etihad early next month, holding a 2-1 lead from February’s first leg.
Should we be successful, we will face a quarter-final against either Juventus of Italy or Lyon of France.
The winners of that tie can look forward to a semi-final against either Napoli, Barcelona, Bayern Munich or Chelsea.
However, City director of football Begiristain insisted his immediate thoughts are all about trying to overcome Real.
“The first step is to try to beat Real Madrid," he said.
"With their experience in this competition they are still strong.
"We are happy to play at the Etihad against Real Madrid but we have to wait of course."
Should City manage to progress to the last eight, it promises to be another tough encounter with the winners of the Lyon v Juventus last 16 tie lying in wait.
And Begiristain says that if City were to reach the quarter-finals, either opponent would present the sternest of tests.
“Both Juventus and Lyon are top teams with plenty of experiences in Europe,” the former Barcelona and Spain star added.
“They will be very, very interesting matches.
“Olympique Lyonnais have good players and Juventus are a big team in Europe,” Begiristain added.
“Both have big experience in Europe. Even Juventus are winning the trophies and domestic trophies so it is one of the treatments of winning the Champions League.
"They are waiting a long time to get this Champions League.
“They have a top squad and they are going to be even more difficult, but of course all the respect to Olympique Lyonnais as they can do it.”